If I would have to select a tour, I would prefer to take a 2-days guided-tour by car from Bucharest.
There are many companies and you can find such tours on Internet.
Think that (train taxi + tips tickets) > price of such tour!
The international airport Henri Coanda is located in Otopeni (30-40 min from Bucharest, depending on traffic) and to get to the train-station from Otopeni you need to travel more than an hour, so I think that you will have to negociate with the taxi-driver (some of them are not very honest about the price of the trip and the "contor" is suddenly "broken" and "impossible to fix"...)
Also in Brasov, you need to move from the train station to the other side of the city, to wait for a crowded bus for Bran and then you need another 40 minutes to reach the end of your destination... To come back and take the train - same story!
If you take the guided-tour by car, is perfectly safe, your luggage will be safe, you will have someone to tell you more about all the Romanian real history/ legends/ tales, you can stop wherever you want to take a picture, you will find the best restaurant/ hotel/... with no effort!
Bucharest deserves at least one-day tour (especially the open-air Village Museum or the wonderful Cotroceni Museum). Also the monumental Palace of Parliament is included in almost every tour of our Capital, but I would recommend Cotroceni Museum which was one of the royal residences (today at Cotroceni Palace is located the PRESIDENCY of Romania, but you cannot visit that wing!).
In two-days trip you can see:
Day 1: Bucharest - Peles Castle and 300 years-old Sinaia Monastery (Sinaia) - Brasov Center - Bran Castle ("Dracula's Castle", but I'm afraid that all vampires flew to Hollywood...) - Sighisoara (one night accomodation).
Day 2: Sighisoara - the only Medieval Citadel still inhabited in the world (UNESCO HERITAGE LIST) - Sibiu (ex- Cultural European Capital of 2007) - the Olt River Valley - Cozia Monastery (orthodox) - Pitesti - Bucharest.
If you prefer the train, you have to be VERY careful about your luggage, wallet... I don't want anyone to panic, but is better than spending your time at Police, isn't it?
ICE HOTEL is only ONE thing to see... in Brasov, Sighisoara, Sibiu there are many-many things/ museums/ the city itself (medieval gates, towers, churches, restaurants, shows, night-life...).
http://www.bucharesttours.ro/brasov-a-sighisoara--2-day-tour.html
http://www.carpatiatour.ro/oferte/detalii/romania_63/incoming_74/transylvania_the_land_of_fairy_tales_345.html
Hoping this will help you to see more beautiful sides of Romania, let me be the first person to wish you: "Welcome to Romania!"
Alexandra Ionescu