I'm in two minds about this...
The first says, for the social experience it would be much better than travelling on your won... However...
For the actual sight seing it would be a lot better and cheaper going on your own...
Depending on how long you can have off and what you enjoy maybe have a look into volunteering in some way. You could always take a month and do a week or two in California volunteering, make a few friends and perhaps tag along for a week or two to places you actually want to visit. Then move somewhere else and do another week or two volunteering...
Any decent volunteering oportunities shouldn't cost you anything and food/accommodation may well be provided. This way youcould spend £1000 (inc flights) and get to spend a couple of months wondering around, with others.
For example, you could copy the "freedom trail" tour they have on their site by doing a weeks voluntering in the north (Maine, New Hampshire, Vermont) and then visiting Boston and that area, then move south to the Carolinas, Viginia or Pensylvania and do another week or twos volunteering and another week or two of travelling round that area with some people you met. Depends what you want to do but if you like wilderness then the Appalachian trail club is one on the east coast you could look into, the West coast and central area have similar clubs (Oregon trail for one).