viamichelin suggest going via birmingham, coventry and luton none of which would be top of my list of places to visit. you could go via oxford instead but roads wouldn't be as good. if you're just looking for somewhere to kip you'd be as well off just stopping in a travelodge near luton or coventry.
I'll second the Stratford on Avon suggestion, stayed over in travel lodge near Birmingham then took in Stratford the next morning.
Warwick is also close by and is a nice city.
You could try the AA route planner to find a listing of the towns you'll be near, you can search it for a route that avoids motorways and is therefore a bit more scenic.
On the return journey I stopped off at Chester, lovely city too.
Oxford isn't far off the M40 either .. or the North Cotswolds area which is sort of between Stradford and Oxford and has lots of nice little villages
M40 is a better bet than the M6/M1 from Birmingham from a traffic point of view in my experience ... so unless you're travelling to North or East London (where the M1 is handier) then it's better to take the M40
If the M4 was not too far out of your way, Newbury is a nice little town, I stayed in the tRavelodge near there last weekend. Handy for London westside/Heathrow. Slim