Sylvia, check the reviews on booking.com:
http://www.booking.com/hotel/it/alexandra.html?aid=318615;label=New_English_EN_MN%3A_Minnesota_23537646145-kSRT0VtFDioJkEc5EAoM0AS91481190265%3Apl%3Ata%3Ap1%3Ap2%3Aac%3Aap1t1%3Aneg;sid=e381fcf056f333421afdca7165b66051;ucfs=1;room1=A,A;dest_type=city;dest_id=-126693;srfid=6dd08907ed9b294927b19e496879dea2e8a655c6X1;highlight_room=
Also Trip Advisor:
https://www.tripadvisor.com/Hotel_Review-g187791-d205841-Reviews-Hotel_Alexandra-Rome_Lazio.html
They're generally positive, and you have to toss off some from ultra-picky tourists on both and one-time posters on TA. Lots of positive comments about the location, and I wouldn't have any hesitation staying there myself. We've stayed a few blocks south of there and had no complaints about the area. Ability to walk to "all" of the sights depends on what sort of walkers you are? What is walkable to one person may not be to another but with just a few exceptions, we've gotten around Rome almost entirely on foot and enjoyed every minute of it.
You will be very close to the Barberini metro stop on line A: useful for jumping on to get to sights close to other metro stops. You will have to change to the B line at Termini to get to those further to the south, like the Colosseum. It's not difficult to do, though. Line A is red on the map in this link, and line B is blue:
http://www.atac.roma.it/files/doc.asp?r=385
A note concerning comments about rooms being small? We've found that European city hotel rooms - unless you go to a premium level - are very often much smaller than we're used to the U.S. so it's not necessarily a failing of this particular accommodation.