The CP Wangfujing (which I would highly recommend for convenience - it allows going for a stroll in the evening and having dinner at restaurants that have English menus, for example) can be quite cheap using Friends and Family rate. That said, yes, there are other hotels that are cheaper and considering you are planning to take cabs/tours anyway, location doesn't matter that much. HI Temple of Heaven is nice and cheap, HIX Temple of Heaven is even cheaper, but there are no restaurants nearby and the hotel itself doesn't have (a decent) one either. HI Downtown, located in the west, is good and well accessibly. Both HIs are older properties. HI Deshengmen is a new property, easily accessible by road to all sights; there are a few restaurants around the corner, but nothing much else to do by foot.
Tours: I can understand that, but be warned that all the major sights (Forbidden city, Tian'anmen Square, Temple of Heaven) are enormous and require a lot of walking inside; few can be covered by 'golf cabs'. You can rent a car for a day (8 hours, 100 km) for as little as 400 CNY (and hiring a cab for the day may even be cheaper), however, this does not include a tour guide. Whether one needs one is another question...