I've owned mine in the city for nearly 3 years, most of the time in the Lincoln Square area. Never had a problem. Hopefully you can get a garage that is attached or at least close enough to wear you sleep so you can hear the alarm go off. I would also get a garage that is your own...and not shared. People's bikes and other property get jacked all the time because their NEIGHBOR left the door open. Ask the landlord if you can put an extra security measure on the door..like a lock so the thieves can't push it up with a floor jack.
The car does get attn, but probably not as much as you think. When I drive to the burbs I get way more looks, comments, etc. There is just more going on in the city in general for people to just be looking at you. This is a good thing.
Obviously, parking on the street is a huge no no....ever. The new ticket company is walking into private lots and writing tickets. Just got a $200 one for tint, and it's not even close to limo.
Above all though, the real issue for me has been worrying about it wherever I go. You will find yourself stressing out about checking out of the grocery store as fast as you can so nobody dings you. That goes for every parking situation. This is the worst part for me.