Back when I was a student, I bought a ticket for 99 dollars** on the Greyhound company's buses, which for six months would let me travel over any of their routes twice, once in each direction. This worked out well. I slept on the bus. I had no luggage, just my toothbrush and my elephant-skin money-belt, and every second or third day would buy new clothes from the surplus stores in the vicinity of the bus stations, and change in the store.

I really enjoyed that tour. It wasn't difficult to plan either. I didn't even have a map or a Greyhound schedule (impossible to carry anyway, it'd be a book several feet thick in the days before the internet on every phone). I'd just take the first bus that was going either roughly west or, on the way back, roughly east, and that way zigzagged my way across the States and saw a lot more than if I'd driven myself from city to city along the interstates. I'd ask people on the bus where it was going and what there was to see when it arrived. I was often invited to their homes. (Later, when I was in advertising, this experience made me the leading authority on how Americans could be expected to react to new products. Virtually all of my college chums and colleagues had never even met Mr and Mrs Middle-America. I'd stand before a massive computer printer folding out sheets of expensive statistical consumer research and announce in tones of ringing certainty what the numbers would tell us and, to the despair of the white-coated techies, I was never wrong. That 99 dollar bus ride was the cheapest and most enlightening classroom I was ever in.)

You could ask if the Greyhound still has that compendium ticket, and take a folding bike in a bag with you for local exploration.

The same mode of travel might apply in other places, though perhaps not as cheaply as in the States. Rail travel in Britain and Europe is vastly overpriced, but you could look into across-border validity of bus passes for those over 70. Here in Ireland they also include free rail travel, and there's a definite permission to use the same Irish bus/rail pass on the British transport in Northern Ireland -- I know someone who used it when he travelled to Northern Ireland where he had his cataracts removed. So it probably works in reverse too. The pass itself in Ireland is automatic, a code on a biometric ID card that the government was once keen on. (One of my late chums, who owned city real estate by the block, was outraged when he turned 70 and a replacement card arrived with a letter pointing out he could ride buses and trains free.)