Have done this within the last 12 months, as DIY. As above says, the old city is very small and easily walked. We parked at the waterfront by the old fort, which is possible to go in for a small amount of money. The old city can be explored by foot, with a decent sized trading area, worth exploring. The old streets are worth exploring to see how people live. Lots of mosques and redundant churches. Plenty of opportunity to get a feel of the place but not full of specific tourist venues.
No idea if tourist bus visits are available - we accessed it from the south.