There are regular local buses from surrounding resorts into Nesebar. If you are on a package holiday in one of the nearby resorts, the rep may try to sell you an excursion to Nesebar on the basis that local buses are unreliable, confusing and expensive; ignore them. You can get buses to Nesebar that are clearly marked in English from numerous bus stops along the main road, and they only cost a few stotinkis.
You can also get a tourist boat from Sunny Beach to Nesebar; this is more expensive and less frequent that the buses.
Roads in and around the old town of Nesebar are quite narrow and cobbled. It is probably wise to park just outside of the town and go by foot. The cobblestones does make wheelchair access quite difficult but some streets have smoother surfaces.
A huge part of the ancient city of Messembria (the old city of Nesebar, located on the ex-island) has sunk under water. When counting the numerous sunken ones, Nesebar becomes the city with most churches per capita in Bulgaria.
The main things to do in Nesebar are to wander around the cobbled streets and visit the churches. In winter museums closed saturday and sunday.
There are numerous shops and stalls selling souvenirs in Nesebar. Most of their stuff is cheap tourist tat, but you can pick up locally produced lace too.
There are loads of restaurants in Nesebar, with a high proportion employing touts to encourage tourists into their premises. These are likely to be more expensive that most restaurants in Bulgaria, and not very good quality. The Tequila Bar is often recommended though.
Zagorka is the national lager and is excellent value and tasty. Kamenitza is also a good beer known nationally in Bulgaria. Burgasko is the local beer but have heard rumors that the quality has declined.
Much of the accommodation around Nesebar is in Sunny Beach, a massive tourist resort to the north of the town.
Nesebar is extremely safe but you may find that the sellers and shopkeepers are very persistent. A lot of the time a shop keeper will insist on following you around the shop and trying to make you try on jewellery clothes etc. A polite but firm "no" usually suffices.
There are regular buses to: