i'm new in the forum, (46 Years, Portuguese living in Lisbon) so i'll try to be very simple in some points.
1. Pensão Londres is fine if you got a good room (street view)
2. Bairro Alto is noisy at night (especially at the weekends)
3. Is in the top of a hill, there are some - but not many- Bus and a Lift (Elevador da Glória).
4. Check if they have a lift in the building (historic buildings)
1. The views,
2. the crowd (young travellers from all over)
3. An amazing bakery near the entry (http://www.cm-lisboa.pt/uploads/pics/tt_address/lxi-3328-01.jpg)
4. At walking distance you have: (Restaurants, Bars, Antique Stores, Sight seeing, Amazing boutiques at «Princepe Real», a underground water cistern built around 1700, and lots more)
My tip for you - and the Forum:
You've got a nice budget for this kind of Hotel (we call this «Pensão», because it has less features). All of this good things you can experience out of you sleeping room. Lisbon is a compact city, is a walkable city - if you got sneakers, you must know that our beutiful pavement is thugh for the feets (https://youtu.be/WBd-fMzXR08).
I send my foreigner friends to: «Hotel», «Pensão» and «Residencial» (this are Keywords) in the area of «Av. Almirante Reis», slightly away from the buzz, but with subway, Bus, Taxi and better: less pricy good service.
I hope this is helpful