lexande

You'll obviously see more if you take more time, but there's nothing wrong with seeing the highlights of a lot of places while only spending a day or two in each. I've taken a number of 10-day trips visiting six or so cities in Europe and found this still leaves enough time to see the most interesting sights in each place, and stay a little longer in whichever you find you like best.

That said, you should probably give up on trying to get to Russia, as that will take a full day on the train each way from any of the other places you list, and furthermore has annoying visa requirements and isn't covered by eurail/interrail passes or served by LCCs.

As has been suggested, you can look at the farecompare map to find the cheapest places in Europe to get to, and then use kayak to find the cheapest flights to them. It could be cheaper to change to an LCC in DUB or elsewhere, but won't necessarily be, and for example there seem to be some reasonably cheap flights from IAD to TXL (Berlin) on kayak.

Once you're there, it should be entirely possible to do Berlin-Prague-Budapest-Romania by train, and is likely to be a lot more pleasant than flying. You could get an open-jaw back from Romania, or use easyjet or SkyEurope to fly back to where you landed originally or to somewhere from which open-jaws are cheaper.

I presume he actually wants to enjoy his trip, so that doesn't sound like a very good plan.