It would probably be wise to call the town info center or chamber of commerce before getting there. There are cities like St. Augustine, FL that offer free parking for Buses and RVs a few blocks from downtown and there are small cities like Savannah, GA where parking for RVs is almost non-existent. Charleston, SC has a parking garage with parking for Buses and RVs on the ground floor, parking is not free.
In large cities, you probably should go to a train/subway station outside the city with parking lots and take the train into the city. In a large city, even if I could find parking on the street, I wouldn't be comfortable leaving it on the street. If there was a parking lot/garage with parking, it would probably outrageously expensive. Charleston, SC's parking garage near the visitors center charges the same for cars and RVs (at least they did the last time we were there).
After contacting the town to find out about parking, I would confirm with Google Maps how much room there really is for parking. We live near St. Simon's Island, GA that actually has street signs directing Buses and RVs to parking in the downtown area. It is street parking and it is shared with everyone else. There aren't spaces specifically for RVs and buses. If it's crowded, there is little chance of finding room even if there aren't any RVs or buses parked.
-Michael