Summers in Novosibirsk are typically warm, but sometimes cold and rainy. Winters can be really cold with temperatures as low as -40° Celsius.
Flights are handled by the Tolmachevo Airport , 16km away from city center. S7 Airlines is the major airline here and have domestic flights to most cities in Russia. Aeroflot also have direct flights from Moscow. Bus #111 connects the airport with the major train station "Novosibirsk-Glavny" (Новосибирск-Главный) and Avtovokzal (Автовокзал), the bus terminal (each 30 min). Bus #112 since 06.2011 connects the airport with shopping mall "Mega" (IKEA). Also minibus #1122 shuttles between the airport and main train station.
Novosibirsk is a major station on the Trans-Siberian Railway, in fact the Vokzal-Glavny (Вокзал-Главный) station is the largest station along the route. This means that there are daily trains avalible from Moscow and Saint-Petersburg with a journey time of 2-3 days. Coming from the other direction, there are direct trains from Beijing, Ulaan Baator and Vladivostok amongst others. Also, Novosibirsk is also the final destination of the Sibirjak express train, the longest train journey originating in the European Union. This weekly train leaves Berlin each Saturday afternoon and arrives Wednesday at lunch time. Apart from the long-distance trains there are plenty of local and regional trains connecting with most nearby cities. Vokzal-Glavny station is very close to the Garina Mikhailovskogo (Гарина Михайловского) Metro stop.
There is a lot of public transport in this city. Everywhere you will pay from 13 to 30 rubles (it depends from your change of transport). Taxis, metro, buses, street railways or trams and so on. Most citizens can't speak even basic English (although almost all of them were taught English in schools). Very often it depends from some English accents of tourists, I mean, misunderstanding each other.
The Metro  is cheap but only runs through the city center and just past the Ob River. Still, for the visitor, you can get to many major destinations from its six major stops, including the main square, Lenin Square, on Krasny Prospekt (Red Avenue).
Lenin Square (city center)
See the Lenin's square with a grey-color monument of Lenin left from Soviet era standing right in front of the Opera and Ballet House which, by the way, is beautiful at night. It is also the largest opera house in Russia. There's also the exact geographical center of former Soviet Union just south of Lenin Square, marked by the Chapel of St. Nicholas, originally built in 1915 to commemorate 300 years of Romanov rule, destroyed in 1930 and rebuilt in 1993. In winter residents build an ice town on the Ob River, and in summer you can go to the beach. Near the city center on Krasny Prospekt,you can also see some excellent works in the Novosibirsk Art Museum and Local Studies Museum. You could also consider the Novosibirsk Regional Puppet Theater (over 70 years old in an interesting historic building), Novosibirsk Circus, and several other theaters. As in every Russian city, there are multiple monuments to heroes of the Great Patriotic War (WWII), including an eternal flame guarded at special ceremonies by youths with replica Kalashnikovs. Those are standard touristic places, but you should definitely make friends with locals to see the "best" parts of the city.
The zoo is one of the largest in Russia (after Novosibirsk had a really tiny one for decades until 90-s). Much money have been invested in the zoo during "prosperous 00-s", thanks to the zoo's devoted director Shilo, a member of the bureaaucrat United Russia party. The zoo is very well-attended and one of the best places to visit that Novosibisk can offer.
A visit to Akademgorodok, built in the 1950s as a mecca for academics but suffering from neglect in the post-Soviet years, is still pleasant as a day trip. This formerly elite institution is located about 30 KM south of the city and features several museums and nice, tree-lined streets.
While you're in the area, you might also visit one of several nice beaches on the Ob Sea, the large body of water created by a dam on the Ob River.
Also south of the city, about 2 km north of Akademgorodok, is the open-air West Siberian Rail Museum. There are about 90 historical trains and rail cars there.
Many foreigners may find Novosibirsk gray and boring and not attractive at all, as tourism system isn't really implemented in the city. You'll never see any buses with tourists visiting the city. Yet Novosibirsk is the third biggest city in Russia, it's probably one of the most not touristic destinations in the country. You won't find a lot of touristic guides and prospects about the city. However, if you are interested in exploring real Russia and Siberia and understanding Russian culture, seeing what life in Russia is like and getting in touch with Russia and Russian household, it's a must visit place. Here are a couple of things you might do while staying there:
1. One of the things you should do is visiting Opera House (Novosibirsk State Academic Opera and Ballet Theater). Here is the link to their web-page http://www.opera-novosibirsk.ru/index.php?locale=en_us. But it's recommended to book tickets in advance. They have very nice operas and ballets and they usually play classic things. Many of the plays are known around the world and it'd be very interesting to see a sort of Siberian interpretation. The Opera House is situated on Lenin Square and you can get there by catching a subway train. There are also a lot of buses and troleybuses running to OperaHouse. The location is very central and you'll easily find it.
2. As there's a lot of snow in Siberia in winter, going skiing or ice skating could be a lot of fun in Novosibirsk. There are a lot of ice arenas in the city. Some of them are free of charge, but those don't usually rent skaters. The ones that rent skaters may be not free of charge. One of the central stadiums is "Spartak", it's quite central.
3. Try some Russian specialties, such as pancakes ("Blini") and "pelmeni"). You can either go cafes or this stuff may be found in many cafes in malls.
Many cafés and restaurants offer paid (and free) Wi-Fi all over the city.
While it's better to stay away from some run-down areas the overall situation is not bad. Pervomayskiy rayon and far-off neighborhoods of Leninskiy and Kirovskiy rayons should be avoided at any time.
The safest place is the center (nearby Lenin Square), stay there and you will be all right.