Hi,

1) The nearest decent neighborhood is Cotroceni ( https://maps.app.goo.gl/CZxC5e6kAbGVQeidA ), four metro stops east of Preciziei. It's an upscale residential area with elegant early 20th century mansions and low rise buildings, relatively a lot of greenery and two parks nearby (Izvor on one end and the Botanical Gardens on the other).

Avoid staying around Preciziei (a drab industrial area with just a couple of office and residential developments) or in the nearby Militari neighborhood (an overcrowded area with mostly high rise Communist era buildings and equally dense recent developments, permanently congested traffic, very few parks).

2) Yes, a monthly pass with unlimited travel on all tram/bus/trolley + metro lines costs 140 lei.

Since you're staying for about three months, you should use an Activ card (these cards can be re-uploaded with the pass each month, unlike the Multiplu card which is non-rechargeable). The Activ card costs 3.7 lei.

You can upload the pass at card machines or the STB manned booths near larger stops. Their locations can be seen on this map: https://www.google.com/maps/d/viewer?mid=1nw1ZJHzIO_2JA3d5PnySq8lxKSb2g9hH&ll=44.44877167041442%2C26.100142773174085&z=11 (grem pins are machines, blue pins are manned booths).

If you're arriving by air, there is a machine and a manned booth at the airport's Arrivals terminal exit, you can do it there.

3) For sites within Romania how are you planning to travel, by car? If you only have weekends it's going to be tiresome to get very far only by road.

In any case you could at least add Sibiu+its surroundings, north-western Muntenia (Targoviste - Campulung Muscel - Curtea de Arges), north-eastern Oltenia (between Ramnicu Valcea - Horezu).

You can also fly to Cluj, Iasi, Oradea, Timisoara, Suceava (for the medieval monasteries in the area) or to Baia Mare (for the old wooden churches and villages in the Maramures region).

For other countries I assume you are planning to fly. By car or public transportation, over a weekend realistically you can only do some sites in northern Bulgaria.

To Greece there are flights to Athens, Thessaloniki (both good for a weekend) and various islands.

To Turkey there are flights to Istanbul (very good for a weekend) and the Antalya area.

Other interesting places in nearby countries you could do by air would be Budapest, Vienna and possibly the Croatian coast (there are some flights to Split).