At the street in Via Candia outside the building at the right side you wil find a supermarket and if you turn on first street on the right there's the large district market opened during the days from 7am to 1.30pm with many desks selling fresh fruit, vegetables, meat, fish etc.
At the parallel street in front of Via Candia there are 2 more supermarkets too and at Via Candia many shops. The bakery in front of the building is very good, there's also one more same side building on the left side very good too.
Cross Via Candia and go straight on you will see the Vatican Museums entrance. If you go on the left side, then at the light turn on the right and follow the Vatican Walls you will get to a large square (risorgimento square) turn on the right again and you will be se Vatican Square Columns.
Before getting to the Square you will find touristic point information. From the Saint Peter's Square at the large street in front you cand take the bus hop on, hop off. From there if you cross the river Tevere and take the Corso Vittorio walk straight on in 10 min more walking you will get to the Navona Square, Campo dei Fiori , also walking a little bit more you could reach the Venezia Square and the Forum (ancient roman ruins).
About restaurants:
around the apartment there are some very good such as the Bersagliere Pizzeria at the Via Candia left side, also the Isola della Pizza in via degli scipioni 45 back side of the cinema Giulio Cesare very simple to find (5 min walk from the aprtment).
In Rome we like so much aperitivos, close to the apartment you can go the Zanzara (Via Crescenzio) go to the risorgimento square (see above) and take the crescenzio street and also go to the Sorpasso in Via Properzio (after the zanzara walk 100 meters more and turn on the right side.
Close to the Pantheon you have to go to Piazza di Pietra where you will find the Salotto 42 at the Square.
From 8pm a lot of people drinking wine or a drink and eating aperitivos. Really amazing!