The blue door is in the first city area, in front of the bank where you get the corresponding key, and you get another yellow key there. There are three yellow keys to find scattered everywhere in the level (to unlock three yellow switches in a row), that you need to find in whatever order you want, one of them is easy to get (on the rooftop that you can reach either with the jetpack or by just climbing up the building), one is intermediate (in the first city section, you visit the bank then the bookstore) and the last one is the hardest of them all and involves going through all the buildings in the second city section to unlock the library
edit - I just realized something annoying, the jetpack allows the player to reach a part of the top of the sprite bridge that he isn't supposed to be able to access. It doesn't affect the gameplay in anyway, it's just a bit ugly and dumb. I think I'm not removing it though, the last couple of fights are way too fun with the jetpack