Getting around, no matter where you're going can be a challenge. Renting a vehicle is always an option, but know in advance that driving in a foriegn country can be "challenging" to say the least. In the UK and a few other countries, you'll be on the other side of the road and it'll take some time getting used to looking in the other direction first when making a right hand turn or crossing intersections.

Public Transit is another good option that I've found to be very efficient in LA, Seattle, Germany, Amsterdam among others. Public transit in many European countries ranges from trams, to subways/skytrain type systems, buses, and full size passenger rail.

Check in advance to see if it might be better to buy a day pass for public transit or pay per trip.

In other places you might consider a day (or multi-day) pass for the hop-on/hop-off buses to get around and see all the sites on your list.

If travelling through Europe, seriously consider one of the EuroRail passes - we saved over 700 Euros with the 5-country, 15 day travel pass.

There are a couple of different rail options over in Europe depending on the country. EuroRail is probably the widest spread option with EuroStar as a good secondary alternative.

Your EuroRail pass also covers a large amount of local transit options (subways, buses, trams, etc) but be sure to check with your hotel/hostel or the EuroRail site before "just using it." The fines for riding without paying a fare are pretty significant.

EuroRail also has a bus network (the big air-conditioned, comfy buses) that will cover some of your connections if rail doesn't make those runs. Pretty comfortable.

If you're only planning on a couple of countries over in Europe, there are a couple of air options that are fairly inexpensive and way faster than the train. Check those options out too. Keep in mind though, that you may pay extra for baggage so factor that into your ticket cost.

Don't exchange currency at a train station or airport. While the rate is excellent, they get you with the 'unadvertised' service fee! In Prague it was 17%!