Hey James, there are a good few airports around Europe which offering great spotting opportunities.
AMSTERDAM Whilst Amsterdam is one of the best for photography angles, etc, it may not be ideal for you as it does not get many 747's (only KLM, Martin Air Cargo and Air China come to mind) and one one daily Emirates A380. It does have plenty of MD-11's though which might be worth considering as they are starting to get retired. You do need a car to get around the spotting places at AMS, unless you are happy spotting from the viewing terrace which is quite large in size and offers a view over most of the gates. Courtyard Hotel (by Marriotts) which is beside the Polderbaan Runway puts you walking distance (3km along a straight road) from the Polderbaan RWY. Alternatively, the Best Western hotel is a very short walk to the Kaagbaan RWY.
FRANKFURT Staying at the Intercity Hotel at Frankfurt Airport puts you only 5 minutes away from a spotting location overlooking both the main RWY's where you will catch the majority of arrivals as well as some aircraft taxing past. Well worth the stay here. Lufthansa has many A380's along with Qantas and Singapore Airlines. The big bonus here are the Lufthansa 747-8I's and the 747-8F's of World cargo airlines and Air Bridge Cargo. Also a good few cargo MD-11F's to see here. FRA also has a viewing terrace at the airport however it is backlit for most of the day.
ZURICH Another great airport for photography angles however very few 747's here and only one daily Singapore A380. Plenty of Swiss A330's and A340's though. Plenty of spotting locations around the airport, with two viewing terraces inside the airport with a bus between them, also bus tours around inside the airport perimeter. Probably better during the summer months. Another good spotting place here is the top of a car park beside the main runway where you are looking down on arriving aircraft, however this spot is only good for weekends. Personally I'd leave ZRH for the summer months.
HEATHROW LHR gets my vote as the airport to visit. Plenty of A380's daily (over 10 from memory from 5 or 6 different airlines), plenty of 747's and A330's aswell. All movements are highly predictable, all arrivals will land on one RWY whilst they depart on an alternative RWY which makes spotting easy. Free transport around the airport perimeter on the local buses also makes getting around easy with plenty of spotting locations available around the airport. All hotels are situated around the perimeter so in most cases you could even spot from your hotel room if you get one facing the airport. LHR also offers the best bang for buck out of all the European Airports as it's the cheapest to get to for us NI folks, and it offers the most movements to spot. I hope this helps a bit!