Urban sniping is an interesting thing. We see sniping really fall into three categories, short, medium, and long range engagements.
Short range engagements are less than "Maximum point blank range" (MPBR) shots. This means that the bullet leaves the barrel and never goes above or below a few inches. Even a 30-30 has an MPBR in excess of 250 meters when you give it a +/- 6 inches.
Medium range engagements are really out to "about double" the MPBR distance for a weapon.
Long range engagements are greater than double the MPBR of a weapon.
If you take the standard 20" AR-15, MPBR is 320 meters with M855 ammunition, less if you want a real +/- 6 inch pipe zero. This means medium engagements are between 300 and 600 meters, and long range is greater than 600 meters.
These numbers are pretty typical for most weapon systems, although the 7.62x39 is a bit less because of the difference in trajectory (about 200 MPBR), and the 22lr is even less than that (about 100 meters MPBR).
The longer your shot, the greater the time of flight, the more wind comes into effect. So the closer you get to your target the greater your chances of success. This is why the "Beltway Snipers" always took their shots inside MPBR distance, and most Iraqi "snipers" do the same.
However, inside of MPBR greatly increases your chances of getting caught. So either you need to cache your weapon in place, or abandon it, or have it able to be broken down and put into an inocuous carrying case like a gym bag or backpack. This is the idea of the "urban sniper rifle", something small enough to make infil and exfil easy.
For that I recommend something different than a bolt action rifle. An AR-10 or AR-15 with a 16~20" barrel. Collapsing buttstock optional since you can take it apart with the push of two pins. Caliber is immaterial, anything from 223 to 308 will work, and all the exotic 6.5 Grendel/6.5 LBC, 6.8 SPC, WSSM's only change the MPBR less than 100 meters either way. If you want one then get one, but caliber is not important compared to skill.
Terrorists are using AK's for urban sniping, skill is more important than equipment. But good equipment is always nice to have.
So, to sum up, the majority of your shots should be in the medium range (longer than MPBR) to maximize your chances of successful infil, shot, exfil. Your weapon needs to be either expendable (a "dump gun") or small enough to not raise suspicions during infil/exfil. A silencer would be nice, but if you set up your hide properly you may not need one.