I've been on an Amsterdam ArenA tour and it was pretty cool, the museum was nice. I found that there is a special walk in stadium tour, no need for reservations. It's about an hour and the guide can explain in English too.
I've also heard that Ajax Experience is cool, not exactly sure what it is but I think it's some kind of museum. It isn't near the stadium though, it's in the city centre. Here's a site you might want to chec out about it:
http://english.ajax.nl/Ajax-Experience/Preview.htm
Ajax will have their first public training on June the 27th, although that might be a bit early.
The other club nearby is AZ in Alkmaar, about an hour away from Amsterdam.
They'll play a couple of teams for pre-season.. These are the teams they'll play against:
14 July: AZ - Istanbulspor (Undecided)
20 July: AZ - MVV Maastricht (Tuitjenhorn, not very far from Alkmaar)
25 July: AZ - Genclerbirgli (Hoorn, also not very far from Alkmaar)
28 July: AZ - Real Mallorca (Home stadium, the match is part of the AZ Fanday, that is why the tickets are free, but I think you need to be associated with the fanclub)
5 August: AZ - Fortuna Düsseldorf (Undecided)
The Eredivisie starts the 11th of August, and Ajax and AZ will play eachother in Amsterdam the first fixture. But I think it will be very difficult to get tickets, because you need a special club-cart to purchase tickets.
If you need more information about Dutch clubs tell me.
