A visit to Arbois is fairly simple as the village is really small. My recommendation would be to visit the Tissot store and then have lunch at Le Bistronome. If you want to really visit and taste then you gotta move a bit. Again, Tissot(Stephane) is amazing as he really excels in all styles. If you’re feeling experimental then there’s so many more to visit, so just say and there’s plenty of nerds here on the board who can help.
If you’re outside the main season, then many places only open very briefly, so check in advance.
Bistrot des Tournelles has a wonderful selection of wines, which are somewhat conservative in their form, but truly unqiue still, and they serve some food.
Bistrot des Claquets is the hang-around spot for the young jura wine crowd, and only now and then is lunch served. You’ll find ‘special’ wines on the shelves along with razor sharp local gems.
For cheese I’d just stop by Essencia. At least in Arbois there’s a fixed selection of wines so you don’t need to deal with the grumpiest shop owner in France, who’s in Essencias Poligny branch.
It’s a beautiful little place.