I am planning on moving to Chicago in the late spring and I am looking for and area of town that is still in the city…cheap…safe…and close to music venues…I am a musician…I am looking for a fun area…with younger people…if anyone has a suggestion…all aid would be very much appreciated…thank you for your time.
Wow. That’s one tall order. It’s been ten years since I moved out of Chicago, so take that for what it’s worth. You could probably find everything you asked for, except for the cheap part. Generally, “cheap” and “safe, in the city, and fun” don’t go together that often. I would guess, that if you could find a college campus area, that might fit your needs. For awhile, I lived near Loyola’s campus in the Edgewater/Rogers Park area, and it wasn’t too bad, but you didn’t have to venture very far to find trouble. Prior to my leaving, I lived in Evanston, which is the first suburb to the North on the lake. Evanston is a college town (N’Western U), on the lake, relatively safe (at least it was), and close enough to the city that you might as well be in it (public trans, etc)
Plus, Evanston is home to the best pizza ever… Carmens!
Stay on the North side. The worst neighborhood in Cubsville is better than the best neighborhood in soxland. 
Where are you moving from? Are you near Chitown now?
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Moving to IMHO.
I’ve also lived in Evanston before, and now live in another Chicago suburb about 45 miles from the city. It still feels too close for me.
If I had to move back to the city, Evanston would probably be my choice. However, you said you were looking for a fun area, and there wasn’t much of that when I was there (1993-1997). The city was the place to go for fun. Fortunately it’s just a 30 minute ride on the el train to get downtown. Oh, and Carmen’s pizza really is good.
The Chicago Police Department has some crime statistics here, so you can check out the relative safety of each neighborhood. Even the nicest areas have some crime, a friend of mine has lived in Lincoln Park for 18 months and her car’s been broken into twice. If you’re into defending yourself from criminals, it’s against the law to own handguns in Chicago.
I don’t know what you would consider cheap, but I’m going to assume you’ll be looking at apartments not houses. A lot of areas that used to be run-down have been gentrified in the last few years with luxury condos and townhouses in the $200K+ range. If you can find a roommate you’ll probably be able to afford something more livable. I would also suggest living on the North side if safety is a higher priority than cheapness. If not, well, stay away from Humboldt Park no matter what.
Good luck, enjoy the city, and watch out for stuff falling off the buildings!
I grew up in Evanston, and I love it, but the rent is too damn expensive! Somewhat cheaper, but still relatively safe: Lincoln Square, parts of Uptown, parts of Lakeview, parts of East Rogers Park…
Lots of the trendy musician types these days live in Bucktown/Wicker Park, but those places have been gentrifying rapidly for that very reason, so it’s getting harder to find cheap apartments. Good luck!
The Wicker Park area (North and Milwaukee) is pretty up and coming, I’ll echo Eva Luna.
I’d say Wicker Park is more up and gone rather than up and coming. You pay a bomb for rents anywhere near there or Bucktown these days. Logan Square is relatively affordable last I checked. You can find some cheap places in Uptown, but that neighborhood is not necessarily the safest (depending on where you’re staying.) Evanston or Rogers Park are great areas, and I’d definitely recommend either of them. If you split an apartment in Evanston with roommates, I’d say you can expect to pay $500/month for your share of the rent. And Evanston these days is a lot livelier (apparently) than when I went to university there. The liquor laws have eased up and it’s become a bit of a bar town these days, with new watering holes springing up on every other block it seems.
I’d say given your description, Evanston is probably the best bet.