I'd say Moreton in Marsh is as good a base as any. Easy to get there by train from London, then the local bus service will enable you to get to Chipping Campden and Broadway, as well as into Stratford upon Avon http://www.johnsonscoaches.co.uk service 21/22
Also http://www.pulhamscoaches.com operate a bus service that would enable you to get to Stow on the Wold and Bourton on the Water (from where you can walk to the Slaughters - prettier than they sound!) service 801
Also very close by is Bourton on the Hill where you will find Batsford Arboretum www.batsarb.co.uk. I think the 801 and 21/22 would drop off there, and there is also a nice walk of between 1 1/2 and 2 miles from Moreton to the arboretum. In the same village there is also Bourton House Garden http://www.bourtonhouse.com which is pretty to visit ( only open between April and October, so should be open when you plan to visit, but not every day so check their website if you are interested). Unfortunately you only get to see the house from outside but it's worth a visit.
Food wise there is an excellent gastro pub in Bourton on the Hill www.horseandgroom.info, as well as numerous places to eat in Moreton and the other villages I have mentioned.t
So you would definitely find more than enough to do to that would fill 3 days, without having to undertake major hikes or bike rides - unless you wanted to. Rest assured there are local taxi services so if public transport let you down you wouldn't be stranded
A car just makes planning easier/flexible, journey times shorter and enables you to get off the beaten track more easily, but you can see from what I have outlined that you'll be far from stuck and travelling by bus you'll get to see some countryside too.
I hope that helps and give ps you some practical local info that will help your plans. Feel free to ask any questions you may have.
Edited: 10 years ago