Want to rent my condo?
In all seriousness, Lincoln Park or Wrigleyville are very good choices. It all depends on what you are looking for in a neighborhood. If you want a big city feel and live in a high-rise, I would suggest Streeterville/River North. Lincoln Park is nice, however it is expensive to live in the prime areas(East of Clark-South of Diversey and North of Armitage. Sheffield/Armitage area is decent and close to DePaul--think smoking hot college chicks If you work-out and looking to join a gym, the DePaul facility is open the public--heard very good things, once again about the chicks. Also rent will be lower in the immediate area since its basically college housing. Wrigleyville will be a mix of people just out of college and families. I live in Wrigleyville and cannot stand being here. However I am 30 and married. When I bought my place 5 years ago, I thought it was the greatest thing ever to be able to stumble home from many many bars--and taco bell. Now it is just annoying. Wicker Park/Bucktown is an interesting area. It was mainly gentrified by the Hipster set. I actually prefer going out in that area rather than my own now. WP/Bucktown is a touch older crowd--think 27/28. Most of the people who live there dislike the LP/LV kids and vice versa. When I was boozing it up all the time with fourteenandoh, we rarely ever went out to WP/Bucktown. It was about a $25 cab ride and we had to commit to stay there all night. Rent would probably be on par with Wrigleyville/Lakeview, and less than LP. Another thing you should consider is how will you be getting around? Im assuming you will take public transit. The EL is usually the better option, when choosing which stop to live closest too. Especially since you are going to Financial District--LaSalle/Jackson. To take a bus there, you will be one of the last stops--probably about 45-60 minute commute during peak times. Train cuts that in half--even quicker on the Blue Line from WP/Bucktown. If you need parking--try and get it with the unit, otherwise stay away from LP. Street parking in LP is very difficult, you will circle for hours at times looking for a spot. Parking in Wrigleyville will be easier, aside from Cubs home games. Bucktown/WP is hit or miss.
I can go on and on about areas--however the best thing for you to do is get to Chicago and hangout/eat/drink/walk around each neighborhood. Do not even start looking at units to rent until you narrow down the hood. Find what is the best for you. I have lived in the city for almost 8 years now. If you have any questions shoot me a PM and I will glad to answer/help out.
Best of luck.