Rogers Park has a nice mix of cultures (not one dimensional), the lake, the Red and Purple Lines. It has more of a mellower, greener feel to it than most places in Chicago. It has some rough pockets. I am strictly an artist and can't speak to the condition of the real estate market their in relation to the other areas in the city, no clue... Keep in mind you are spending five years of your life somewhere, not just investing.
Edgewater is a great area to consider as well - incredible access to the Red Line, convenient to Lake Shore Drive - many transportation options, plus 1 bedroom units are plentiful in and around the $150K price range.
I hope that helps!
It might be hard to find anything in that price range in Wicker Park, Bucktown, etc. The areas that were somewhat 'iffy' in the city such as Logan Sq., Pilsen, Albany Park, Garfied Park, and the like have dropped significantly in price and may be good bargains right now. I personally like Pilsen a lot but you have to try to find one of the blocks that are relatively gang-free. It is close to the Pink Line and the Blue Line. If you're looking for a well thought answer to your question you should post some more search parameters. Some of the more savvy re-litters that cruise the site could be a good resource for you. Good luck!
I find that the main critiria you want is one that has easy access to public transportation and/or access to main expressways and walking distance to restaurants/shopping. I would think that Lakeview, Jefferson Park, Portage Park, Logan Square and Bucktown areas are all excellent areas to try and find a one bedroom condo. Especially in todays market and with an investment of at least five years will help you.