It's not money or time, it's attitude and self-image.
I recently wandered Paris with a video camera, but I didn't feel like a tourist because I've been there many times, am comfortable in the city, and was having a good time.
And it's a good thing I could afford a hotel room with a toilet, because my friend and I both got food poisoning and were in that toilet most of one night.
New Yorkers know visitors to their city instantly by their walking pace. I'm happy to supply directions when asked, but when you stop dead in the middle of a busy sidewalk to read your guidebook, you really piss me off. The good visitor is sensitive to the ways of the place he's visiting. The bad visitor tries to bring his home along.
Wherever you go, there you are.