The 4th of July is one of the busiest times here. Especially with the 4th landing on a Monday. I don't think you will find too much under 200. I doubt you will find anything under 150. The less expensive hotels will be in an area called New Town but you will need some means of transportation to get to old town which is where the tourist section is. It has most of the museums, galleries, tours, bars, restaurants etc.