Poltava is also called a cultural capital because of its colourful history and many famous Ukrainians who were born in Poltava. Native citizens often follow this idea, being proud of their city and calling it "a city where one wants to live in". Off course, trying to keep this rate: there are many sites of architecture, museums, universities, elementary schools, cinemas, theatres and so on. Apart from that, city is often referred as "green" as there are many parks, gardens and other recreational areas. In the recent years the municipal administration considered itself as being responsible to make the city centre clear and looking more like a European rather than Soviet city.
Languages spoken are Russian and Ukrainian. (Latter is official and first is more widely spoken). However most people understand and are able to talk both. English isn't widely known, but many people (especially young people) would make their best attempt to understand you. You may be glad to know that some people you talk to are quite fluent in English (or German, French), as these languages have been studied at school.
Train and bus are the only reasonable ways to get to Poltava (unless you have your own car), and ticket price is roughly equal.
Four railway lines coming out west, east, south and southeast from Poltava, connect it with Kyiv, Kharkiv and other Ukrainian cities. Usually there would be a few trains per day to your selected destination, see the website of Ukrzaliznytsia (Ukrainian railways) for timetable and ticket prices.
There are 2 railway stations: Poltava-Kyivs'ka (Полтава-Київська, also: Київський вокзал, Kyivs'ky vokzal) and Poltava-Pivdenna (Полтава-Південна, Південний вокзал, Pivdenny vokzal). Watch your timetable/ticket carefully, as train may stop only at one of those stations, or both. It would be a good idea for you to buy tickets for your next train (if you haven't bought them in advance) immediately upon your arrival. Both railway stations are well connected with city transport (bus/trolley), however between 10PM and 6AM taxi is the only option.
Bus connection with other cities is fine, especially along E40 road (Poltava is midway between Kyiv and Kharkiv): buses usually arrive/depart every hour or a few. It will take you 5 hours to get from Kyiv or 3 hours from Kharkiv. There are a few different carriers on these routes:
You need to buy ticket at the bus station, and then better keep it with you, ticket control is possible. You would arrive at the (only one) inter-city bus station called Avtovokzal (Автовокзал), which is connected with municipal bus/trolley routes. Note again, that between 10PM and 6AM you'd need to get a taxi.
Poltava has fine road connection in most directions: west (E40 to Kiev), east (E40 to Kharkiv), southwest (E577 to Kremenchuk), north (to Hadyach), northeast (to Kotel'va and Russian boundary) and southeast (to Krasnograd, connection with E105 Moscow-Kharkiv-Simferopol road).
Do not go along other minor roads indicated on the map unless you know it's fine (otherwise you may experience bad road quality or get lost somewhere in rural area).
Not possible (there is an airport in Suprunivka, 5km west of Poltava, however no regular passenger service is available).
It would be a good idea to have an aquaintance with a bilingual local person who will give you advice on how & where to go around Poltava. But if you don't have one, you can ask for help at local English-speaking message board en.poltavaforum.com
Notice that most of city transport is operating between 6AM and 10PM on major routes, and only until 8-9PM to suburbs. During hours different from this, prefer taxi. There are crowdy routes, where you may not be able to take a seat. During rush hours (6-9 AM, 5-6PM and possibly throughout the day on suburb routes) you may loss up to 1 hour of your time due to municipal transport being filled up. Be aware of suburb routes as well as of the dates of holidays/other celebrations, where serious delays are likely. In trolleys, buses and marshrutkas you pay a single fixed price for each trip at each vehicle, no matter how far away you go (within city limits).
Poltava is relatively small city, where it is possible to cross it one border to another in 1.5 hours. If you're walking around downtown & historical centre (called simply "centre" - "центр"), you're 30 minutes away from any destination within it. So if you know where to go across centre, you may not use transport at all. However, for safety reasons, don't walk by foot to distant suburbs, if you don't know your way or if it is late evening/night.
Bear in mind that the bottom part of the city (Подол) near Vorskla river and Yuznaya Train station is situated really deep down, so walking up to the train station can be VERY tiresome.
By bus / marshrutka
There are 62 bus routes, connecting most districts of the city. Most often it is an optimal way to get around. Both bus and marshrutka cost 1.75 hryvna ($0.22), no matter how far you go. The difference is that buses are larger (yellow minibuses are considered buses too) and you pay money to conductor who asks you; marshrutkas are small minivans where you pay directly to the driver. Don't rely on the fact that you can enter/exit marshutka outside from official bus stops: it is sometimes possible, but actually prohibited by law.
There are 11 trolley routes across the city. This is the cheapest kind of transport, however particularly slow and often crowded, sometimes delayed. Ticket costs 1 hryvna ($0.12), payed to a conductor, who will ask you soon after you enter the trolley.
Other routes are: listed here
It is recommended to order a taxi by phone, not to hire somewhere on the street. This way you'll be safer, and meet better service and possibly lower price. See for phone number and car number written down on the car - so you will differ between taxi service and unlicensed individual. Costs from 15 to 35 hryvnas (2-4 US$) across the city, or more if you go to several locations. You pay for kilometers, not minutes, however additional costs include waiting time, distant areas.
Probably, the main attraction is the Poltava Battle History Museum 
The museum and the Swedish cemetery are located just 5 km north-east of city. There are several marshrutka buses going via Zygina Square, as well as buses 4 and 5 right to the bus stop «The museum of the history of Poltava Battle»
Hours: Sun, Tue-Thu: 9.00-17.00, Fr: 9.00-16.00 Mo: closed.
There are many other museums, mainly dedicated to famous writers and cultural workers 
Tourist Hotel (готель "Турист"), Soviet-built hotel, but may improved since then. Situated at the bank of Vorskla river, though it is a bit more distant from the city centre (10 minutes by bus or 30-40 minutes by foot) There are a few more budget hotels, hostels etc.
Palazzo Hotel ("Палаццо"), 4-star, ;
Gallery Hotel ("Галерея");
Alleya Grand Hotel ("Алея Ґранд");
Hotel Eurolux ("Готель Євролюкс"), ;
Those three are high standard by Ukrainian means, and have central location less than 15 minutes walk from most sights (museums, monuments, theatre).
Dykan'ka (ua:Диканька), a small town 30km north of Poltava, easily reached by road. Some historical sites and fine restaurants. Also famous as a site mentioned in Evenings on a Farm Near Dikanka (Vechory na khutori blyz Dykan'ky), a story by Nikolai Gogol. If you want to see some landscapes typical for Poltavs'ka oblast, apart from crops, an ancient oak wood is just next to Dykan'ka.
Opishne (ua:Опішне, ru:Опошня), another small town 50km north of Poltava, famous for its pottery. See the National Museum of Ukrainian Pottery in Opishne .