Arriving early in the morning is well worth the effort! You beat the crowds - and, understandably, there are many during the summer season. Another advantage is that you can scope out the place for cafes, restaraunts, and remarkable views. In 1983 Old Nesebâr was declared a UNESCO Historical Site.
Old Nesebar sits on a pennisula, and the only access is via the walkable causeway from the new town. On the causeway to Old Nesebâr, a windmill welcomes you. Nesebâr's fortress walls (3rd-4th century) open up and welcome you to into Old town.
With its history dating back to circa 6th century BCE, Nesebâr has a lot to offer. Once home to over forty churches spanning from the 8th century to late 19th, today roughly a dozen remain - some restored to its original beauty, others preserved as "ruins." The following are musts: Sveti Ivan Krustitel" church (10 - 11 c.), "Sveti Arhangeli Mihail I Gavrail" (13 c.), "Pantokrator" (14 c.), "Sveti Ivan Neosveteni" (14 c.), "Sveti Todor," "Sveta Paraskeva" and ending with the "Sveti Stefan" basilica.
Nesebâr is home to about 60 houses that are designated as historic in architectural style (Bulgarian National Revival mid to late 18th century). Two worth visiting are: Captain's house (Kapitanskata kushta) and Mouskoyani's house (Muskojanata kushta).
This orientation walk is about an hour and a half. After the walk-a-bout, sit down and have breakfast at one of the numorous cafes. Coffee or tea in hand, you can begin to watch the locals prepare for the tourists and then when the museums, galleries, and the aforementioned revival houses open - you are there rearing to go!