24 hours in central Romania

Have I picked a good city for what I am after in central Romania, or do you have a better suggestion?

Brasov is a very good choice (check photos). Sibiu would have been interesting too, but trains to it from Bucharest are somewhat less frequent (and they pass through Brasov anyway).

Is the hike up Tampa Mountain easily marked and safe to do alone?

There are several reasonably well marked paths and they're not very complicated routes, so it's safe.

Also, if I plan to do a tour of the Palace of the Parliament in Bucuresti first thing in the morning (tours start at 10:00 but I understand there may be a wait), will I be able to get a train to Brasov at 1:00pm without having to rush?

Yes, especially if you use the subway.

How long will it take to take public transit from the Palace to Gara de Nord?

By subway 15-20 minutes; get on line M1 at "Izvor" station (it's across the park from the Palace's tourist entrance) and get off at "Gara de Nord" station.

Thanks a lot, you've been very helpful :)

Hello,

I am from Brasov and I can give you some tips. Tampa montain is easily marked and safe (there ar also many roads that lead to the top). There are many peoples who climb it daily.
You will make about 60 minutes to the top (my record is 45 minutes). The panorama is great.

Also you can visit Poiana Brasov (a winter resort). To reach it you have to take a bus from the city center (the bus with the number 20. Be careful, it has a special ticker - price ~70 cents).