St Albans — 20 minutes by train, St Albans has Roman ruins (Verulamium), a Norman cathedral, and one of the best-preserved medieval city centres in southeast England. An easy and rewarding half-day from Luton.
Woburn Abbey and Safari Park — about 20 minutes by car, Woburn Abbey is a stately home with fine art collections, and the adjacent safari park is one of the better ones in England. Good for families.
Bedford — 30 minutes by train, Bedford has a pleasant riverside, good museums, and strong connections to John Bunyan (author of The Pilgrim's Progress), who was born nearby. The town is more attractive than Luton and worth an afternoon.
London — 35–40 minutes by Thameslink from Luton Airport Parkway to St Pancras. The obvious day trip, and one of the fastest connections from any English regional town to central London.