There is a Holiday Inn Express Exeter East, which is within walking distance of Devon Heritage centre. (Literally across the road) We stayed there years ago, very convenient for research, and park and ride.(you can use the bus, even though your car in the car park of Holiday Inn, you have to pay anyway.)
Check it out on line. Good luck with your plans, dont forget to keep your itinerary and details in your hand luggage (just in case!)Our luggage went astray on trip to canada, luckily had details of the places we were staying in etc in hand luggage!got the luggage back next day.