Can't say I've done much European travelling myself, but this video
does a great job of explaining things. It covers PortAventura, Liseberg, Disneyland Paris, Parc Asterix, Gardaland, Europa Park, Efteling, Phantasialand, Heide Park, Tivoli Gardens, Bakken, and Tayto Park. It's around 18 months old, so you'll need to do some research to check it's all still correct, but it'll give you the key details. You can get to pretty much any of the major parks by public transport with varying degrees of ease, with some of the parks closer to the city (notably Liseberg, Disneyland Paris, Tivoli and Bakken), being surprisingly simple. Europa Park and Tayto Park are probably the hardest on the list to get to via public transport, but it's all doable.
Burniel | Great at theme park knowledge, not so great at designing signatures.