We just left Mildenhall (lived in Thetford) and there was so much I wanted to do that we never did. Join the National Trust one year and English Heritage another and check out all the local places. There are also some other air force bases you can stay at (RAF Fairford and RAF Croughton) that are close to other tourist attractions such as Warwick Castle, Kenilworth Castle, Stonehenge, Blenheim Palace. You can also stay at the Royal Naval accomidations. Below I've pasted some info from an e-mail to one of my friends. Oh, also there's a Pick Your Own Strawberries up in Isleham (maybe 10 minutes from Mildenhall). My kids loved that. They have raspberries and other berries too.
We can stay in TLF at RAF Fairford, RAF Croughton, and RAF Mawgan (they all have an American presence). Fairford and Croughton are both in the Cotswolds area. They aren't very big, but you can find lodging there. We've only been to Fariford. Their commissary has very limited hours and their lodging desk closes after I think 9pm (not positive, you'd want to check for certain) but they will leave your room key with the guard at the gate if you arrange to arrive after they are closed. I've heard that Croughton has nicer TLF. Their front desk also closes in the evenings and on the weekends. I know nothing about Mawgan except that there's an American presence and we can stay there. I think it is down on the coast over by Wales.
We can also stay at some of the British Navy lodging facilities. Here's a website for more info.
http://www.rncom.mod.uk/templates/Housing.cfm?id=509
Helensburgh is up in Scotland. There's a minimum of a two night stay and you have to clean the place yourself before you leave. I've never stayed there, but I've heard from people that it's a good deal. I think you might have to bring your own bed sheets and towels but they have pots and pans. If you scroll down to the bottom there is a separate website for The Services Cotswold Centere. I think this is similar to the Royal Navy lodging in that you have to clean after yourself and bring your own linens but it is only 10 GBP a night!
If you want to stay somewhere where there is not military lodging, look for a Premier Inn. It has family rooms that are larger and nicer and you pay a family rate instead of per person.
These are good websites to print driving direction off of:
http://www.theaa.com/travelwatch/planner_main.jsp (UK only)
http://www.viamichelin.com/viamichelin/int/tpl/hme/MaHome... (for Europe too)
If you want to take a ferry to the mainland, my friend says it's cheaper to buy them on-line than when you get there. Also, because traffic can get hairy over here, she recommended buying one for later than your plan on being there. If you're there early and they have space, they'll let you go early. If you're late, you're out your $ and have to buy another ticket.
You can join the English Heritage http://www.english-heritage.org.uk/ and or The National Trust http://www.nationaltrust.org.uk/main/w-index.htm for free or discounted admission and guidebooks and maps. If you go to their websites, you can search for local places to visit. We are in East Anglia or the East of England.
Some ideas for staying fairly close to home are: Oxborough Hall (between Downham Market and Thetford), Sutton Hoo (Ipswich), Duxford Air Museum (Cambridge), Castle Acre Castle and Castle Acre Priory (just nort of Swaffam), Grimes Graves (by Thetford, not good for small children).