I've been lucky enough to go to Silverstone 4 times (5 as of next year), Spa, Monaco, Austria, and Monza. Here's my personal short summary for each:
Silverstone - Best for atmosphere, loads to do in terms of concerts and the campsites are great fun. Very expensive (will get onto that in a second). Plenty of big screens to watch the action from wherever you end up sitting. Can get on the track afterwards for podiums, track walks etc. Obviously convenient if you live in England. Can take your own cans of beer in, but no glass. 4/5
Spa - Amazing scenery and track, not as much to do as Silverstone in terms of entertainment but still has the usual f1 fanzone stuff. Me and my parents drove to Spa, and including fuel, return ferries from Newcastle to Amsterdam, 3 day grandstand tickets and spending money came to about 3/4 of the price of Silverstone so make of that what you will. Solid transport links including shuttle busses from nearby campsites. Again lots of screens. Can get on the track after the race for podiums, track walks etc. Campsites are great atmosphere. Can take your own cans of beer in, but no glass. 3.5/5
Monaco - Race day only general admission ticket, ended up sitting at turn 12. Great for seeing the cars up close and personal, but terrible from an overall perspective of seeing the race. Hardly any screens, and the ones that are there are difficult to see from certain angles. Not too bad to get to (we stayed on a campsite in Nice). Nothing happens after the race (and there isn't any access for track walks etc) for quite some time (like several hours) then the track is opened up and various pop up bars and stuff appear. Essentially from turn 12 to the main straight turns into a big nightclub. Mint atmosphere, expensive as you can imagine it would be at Monaco. Can take your own cans of beer in, but no glass. 3/5
Austria - Possibly my favourite European race that I've been to, no doubt helped by the fact that when I went this year it was absolutely red hot, so that helped. Campsites and what not are all located right at the track which is brilliant, and there's an onsite small supermarket + a massive supermarket just down the road. Excellent scenery and track, with lot's of vantage points where you can see most of the track even with a general admission ticket only. Also lots of onsite entertainment on the campsites in terms of pubs, bars, 'nightclubs' (re: big tents with DJs etc). Probably the most 'festival' like vibe grand prix I've been to. The red bull museum is free to enter and they have various cars and stuff on display. Cost wise was about halfway between Silverstone and Spa. We had the same travel arrangements as Spa (ferry from Newcastle to Amsterdam and drive to Spielberg) so the cost is pretty good when you take into account the extra fuel as it is considerably further than Belgium. Can take your own cans of beer in, but no glass. Would fully recommend this one! 4.5/5.
Monza - My least favourite European race that I've been to. We stayed in Milan, transport links were fine and easy to manage. Scenery wise there isn't much as it's in a large national park and is quite flat. One of the most annoying things at this Grand Prix was that you can't take any alcohol in full stop. They do bag searches quite rigorously on the Friday and Saturday, not so much on the Sunday due to the volume of people. But still a long way to bring cans only to have them confiscated. They also take the caps off any plastic bottles you have. What we did was take spirits in plastic bottles and had a stash of spare bottle caps in our pockets, this meant we only had to buy mixers. If you don't drink obviously it's not an issue, but for us it was quite a big thing and wasn't communicated very clearly before hand which was annoying as we had brought beers on the Friday (working on the assumption that previous races we had attended allowed you to take them in). As a result of this, if you don't like spirits but do like beer, then get ready to fork out for it as it is very expensive once inside the circuit. The circuit itself is good for walking around, and you can see a lot of it with just general admission tickets. Track is open after the race (as I'm sure you've seen on TV for the podiums etc). After the race there is zero entertainment. The place is immediately stripped down and everyone asked to leave the park. 2.5/5