By car, the best place to start is either Toddington or Cheltenham, both have free car parks (Winchcombe also has one, but it's very small and depending on the day of the week you might not get a space).
In terms of accommodation, there will be hotels and B&Bs in Broadway (probably quite expensive), at least one B&B in Toddington (pretty much next to the station), B&Bs (and probably at least one hotel) in Winchcombe (again, likely to be expensive), I know of at least one B&B near Gotherington (Pardon Hill Farm, a pleasant walk from the stations across a few fields) (beware, the village of Gotherington is some distance from the station!). There are plenty of accommodation options in Cheltenham, ranging from cheap hotels to expensive hotels etc.
As you'll have access to a car, it may be worth looking at staying somewhere slightly further afield. For example, if you're coming from the north east, the Premier Inn on the Evesham bypass may be convenient and cheaper.