Estonia, Latvia, Lithuania, and Poland

Safety is relative - it all depends on areas they are in and how late they stay out. Riga seems to be a hot spot for parties with lots of folks from the UK flying in.

Can't speak about hostels as we stayed in hotels. There is very limited train services in the Baltics - Poland is different. They will probably have to rely on buses for getting around. Check out Eurolines and some of the other bus companies.

We were in these areas 5 or 6 years ago and found them much cheaper than the cities in Western Europe. With the advent of LCC flying into these countries, the number of tourists are up and this will probably have increased the prices. However, I would still think these areas are cheaper than Prague or Budapest.

Others who have had more recent experiences may be able to confirm or correct this.

Yes, at least as of two years ago, these countries were still far cheaper than the West, including transport, lodging and food. Poland has rail connections for most of the cities, although the quality of the rail services varies from clean and fast to dirty and slow. You can link to the two major cities in Lithuania (Kaunus and Vilnius) via rail from Poland, but you may have to rely on bus service for Estonia and Latvia.

I can only speak for Poland, as I lived here for several months in 2007. It was much less expensive than visiting other parts of Europe - especially compared to Ireland and the UK. However, Poland is not as inexpensive as you might imagine, particularly because it has a steady flow of tourists from these wealthier countries who are ready to spend lots of quick cash for stag parties and other wild get-away weekends.

I never felt unsafe in Poland, but I did know several students who got mugged. Krakow is a provincial city, but a city, and it is not any more or less safe than any other parts of the world. It tends to feel shut-down after about 9 pm, so I recommend getting back inside by about then. If you miss the last tram, you will have to walk back to your hotel or hostel, possibly down poorly lit streets, and this is the time that two girls could find themselves in danger. Really, it is just a matter of common sense: stay where it is lit, don't go out alone, and don't stay out late when there are few people on the street.

Warsaw is much bigger; coming from a bigger city, I felt safer there. However, the concerns are the same. In Warsaw, avoid going to the black market in the stadium - it offers lots of good deals but is prime pickpocketing territory. Also, keep an eye out for areas that appear to have lots of patrol cops or private security men. Sometimes they barricade areas if there is a major sporting event or other rioting concern; just avoid it and move on.

As for transportation, taking the train is relatively easy if you are staying on the beaten path. Trains are faster between major cities and less expensive and slower into the countryside. Some visits, like to the Tatry Mountains, may be cheaper by bus, depending on the day and the schedule.

There are safe hostels in all countries. You can read about them on this page. You can also read opinions about trains here to.

Why don't you do a google search for "hostels Tallinn" and read about them. Note the cost. To convert to dollars, go to oanda.com and ask for a cheat sheet for each currency you will be using.

Search for hostels in each city you will visit. I have stayed in them for over 20 years all over the world.

Many now have private rooms with bath in addition to dorms which are much cheaper.

As a Lithuanian, I can second the point about checking out inyourpocket.com
I read one that an American friend of mine visiting Vilnius had bought, just to see how accurate it was. I found the commentary witty and incredibly on target. They will not sugar coat stuff and tell you what clubs are gritty and dangerous, what places are rip offs and basically give you some real insight that comes from living in Vilnius for a few years. Definitely worth a read.
Where are you visiting in Lithuania?