You can't do Sofia as a day trip by train from Bucharest. Even if you do an overnight stay in Sofia, it would leave you no time to actually explore the city as you'd arrive in the evening and need to depart the next morning again! Sadly, links to Bulgaria aren't great for day trips with only a single daily train crossing the border.. If you don't mind an overnight, then only Ruse in Bulgaria is feasible. It's a pleasant town on the banks of the Danube, not much to see in terms of sights, but some good bars and restaurants and a pedestrianised city centre and riverside promenade to walk around.

Even within Romania, distances are large and travel times are slow due to the often bad quality infrastructure (ageing railway lines, lack of motorways). You can't compare it with London or Western European countries like Belgium or Germany where you'd always find a lot of great sights and destinations within a short drive or train ride.

The most obvious day trip to make from Bucharest is either to Sinaia or to Brasov. Sinaia (1.5 hour one-way by train, multiple departures by multiple train operators a day) is the most famous of the mountain resorts in the Prahova Valley in the Carpathians. Visit beautiful Peleș Castle, the monastery, stroll around the town centre, or even take the cable car high into the mountains (if the weather and visibility is good) for some nice views and easy hiking on top of the ridge.

A bit further away (2.5 hour one-way) in the same direction is Brașov with its highly picturesque city centre and scenic location in between the Carpathian foothills. Its one of the old Saxon cities of Transylvania and it has a bit of a German flair with its old town houses and impressive Black Church. Good restaurants, bars. Can be done as a day trip, but also makes for a great overnight trip. On your way, you'd cross the Carpathian Mountains and will have some nice views from the train window.

Also cool is the Slanic salt mine, located 208 metres underground. You'd need to change trains in Ploiești most likely, with the total journey taking you 2.5 hours one-way. Alternatively, visit Constanta on the Black Sea coast (2 to 2.5 hours one-way), although personally I think Brașov would make for a far more interesting trip.

If you have any more questions regarding Bucharest or any nearby sights or transportation, don't hesitate to ask!