Is it better to buy a pass for local inner-city transportation (like the subway or bus) for however long I'm staying in a certain place, or should I buy single tickets for individual trips? Basically what I'm asking is to find the cheapest route.

I like walking too. Walking is good and cheap.

It really depends how much you're going to use it!

I almost always buy a weekly/whatever pass for local metro options when I go someplace, but that's because I usually spend a decent chunk of time in the city and want to go alllll over by myself instead of getting on some tour.

Depends! I like to get the Zone 1 & 2 card for the London Underground-- even though I walk everywhere it's great to have and it's not that expensive, I think 4 pounds or something, and it really can be worth it if you start to get pissed on and you're at Hyde Park wanting to get to St. Paul's Cathedral...

In Paris I'll usually buy a carnet of 10 metro tickets or a day ticket. The only problem with that is that the tickets are *very* small and easy to lose but if you're careful it's not a big deal. I found I walked a little more in Paris than in London (because in London I was going to out-of-the-way areas) so the carnet worked out a little better for me. They do have a weekly one called the Carte Orange but you can only get it on Mondays I think. If you're spending more time there it's absolutely worth it.

I bought a three day pass in budapest for about $12 and it was the best investment I made. You can get anywhere you need using the subway, trams, and busses without any problem. Good for going to the citadel, palace, mathias church, parliament and then hitting the baths at the end of the day if your only staying for a couple of days. Also is a quick way to get to train stations at 7AM.

I like to get the passes if I'm going to be some place for a couple of days, too. They are usually a good value and a lot easier to manage than fiddling with change or making sure you have the right ticket, validated properly, etc. We do a lot of walking when we travel, but it's nice to have the option of hopping on a bus if the weather turns bad or if your feet hurt! If you have the pass, you won't think twice about catching a ride, and may do more stuff out of the centre, just because it's easy to get there.