I won't miss Lincoln Park. At all. It's the ritsy, yuppified neighborhood towards the lake and downtown from here. Parking is terrible, everything is expensive (especially rent), and I just don't fit in. Everything's too tall, costs too much money, and even if it didn't cost too much money I wouldn't want to go there! There are some nice stores, but nothing that I can't find somewhere else. I actually can't think of one thing in Lincoln Park (the neighborhood) that I will really miss. I know there are good things there (DePaul students especially can probably come up with a long list) but in my time here in Chicago I haven't stumbled across anything there I will really remember fondly.
I will miss Lincoln Square. It's the neighborhood I live in now. It's located around Western and Lawrence (The Western stop on the Brown Line) and has one of the coolest, psudo-european neighborhoods in the city with a quaint shopping street full of German boutiques and european delis (Meyers, Merz Apothecary). There's a great square with a fountain, a classy indoor/outdoor cafe on the square (Cafe Selmarie), a creative toy store (Timeless Toys), one of the best burrito joints ever (Garcia's), at least two independent coffee shops (The Grind and The Perfect Cup), a comics shop, at least 3 24-hour diners, a cheese shop (The Cheese Stands Alone), a movie theatre (The Davis), a used toys/collectible store (Quake Collectibles), a library, the Old Town School of Folk Music, tons of great restaurants... and much, much more. And to top it off, while it's got a "cool" vibe, it doesn't have the same kind of trendy gentrification vibe that other neighborhoods have. It also has a great statue of pre-beard Abraham Lincoln, sealing it's place as the best Lincoln-named neighborhood in Chicago.
Hat's off to you, Lincoln Square! (And rats off to you, Lincoln Park!)