I have been to Sheki twice and I'm not really a fan. There is a nearby airport, Ganja, which has international flights so before I figured I'll fly in from there and then take a bus ride to Baku. That does work. This time I had a car and I also wanted to see the rest of eastern Azerbaijan so Sheki is an obvious location because it's a) out of the "danger" zones, b) has maaaaany hotels and c) isn't exactly bad. The bus trip to Baku was a good 6 hours so do plan accordingly.

On my second trip I mainly wanted to see Sheki's Palace again. It's a wonderful place and surely the highlight of the town. However, they sort of rush you through the place. I literally had to queue longer than going through and the price isn't peanuts. While I do recommend going inside I have to recommendations: look at the entire place from the outside. This is where photos are allowed (not inside). Second would be to actually take a guided tour. It will cost you extra but then you aren't on the rushed tour through. I would have been a bit jealous of the couple that did have the private (English) tour but as I already went through this place before and thus I didn't think twice about it.

For the rest of your time I suggest you just explore the eastern part of the old city by whichever way you like. Cars tend to stay on the paved main road rather than the old steep cobble streets. On these you will see old designs from just plain houses, Soviet style influence included, and mosques. They are generally all closed but you get to see the best part from the street. My hotel was also an old building and you can see by the large inner court, super high walls and they even had peacocks roaming around inside - better than seeing the palace!!