I think it's ok to change shoes. I used to live in NYC, and walked to and from work. It just wasn't practical for me to do that in heels. It tore up my feet, and it was really hard on the shoes too. The one pair that I would wear to walk to and from work was a pair of 2" Ferragamos. I loved those shoes (but eventually just wore them out).
I would just get a pair of cute, comfortable flats and then change into my real shoes when I got to the office. I usually keep a pair of comfortable flats with me at all times. I have a pair under my desk, and I usually carry a large enough bag that it's no big deal to toss in a pair of flats. Maybe I'm just a weirdo, but sometimes I'll get invited to an impromptu lunch that involves quite a bit of walking. I feel like it would be ridiculous to say, no, I'm sorry, I can't go to lunch with you because I like to wear ridiculous shoes that I can barely walk in. So I'll just change into a pair of cute flats - problem solved.
I think the best shoes to start with are full, closed toe pumps. They offer the most support. I think that closed-toe mules are the worst. To try to discern what will work (which is more of an art than a science), wear the shoes for a long time in the store. Walk around a lot. Try to walk on non-carpeted surfaces. If they hurt at all (other than being generally tight - leather stretches so much), move on. If they hurt in the store, there is no way that you're going to function in the real world. Invest in better brands - Ferragamo are very comfortable, Manolos too. There usually is a significant quality/comfort difference. Try on lots of brands so that you can get a feel for the quality of each. It's going to be personal to you and your foot. For example, with sneakers, I know tons of people who love New Balance. I hate them, they just don't work for me.
Good luck!
I do stress using cute flats - nothing is less chic than clomping in with a big ole pair of sneakers...