Museums and traditional markets of Tehran are located in downtown Tehran and you will need to use the city center hotels for easy access to these places. Ferdowsi Hotel and Hoveyzeh Hotel can be good options. Shiraz Hotel in Tehran and Asareh Hotel are also cheaper options in the city center. For dinner, there are many restaurants in the downtown that you can use, but top and first level restaurants like Nayeb Restaurant are more in the north of the city of Tehran. Then, either you should forget the first-level meal or pass the distance between the city center and the north of the city.
We have a better suggestion. You do not have to book the hotels in the city center to access to the museum and market. Anywhere in Tehran you reside, you are maximum 45 minutes distant from the museums and markets of the city. You can book a hotel in the north and benefit from its advantages like wider roads, tranquil and quieter surroundings and more luxurious environment, good restaurants and cafes, etc. and go to the downtown to see museums and market in the city center whenever you want. The downtown hotels are usually very crowded and apart from a few cases, they do not have a very relaxed atmosphere.