I recommend you to get "Where to Watch Birds in Holland, Belgium & Northern France" to find out how to reach specific locations, although it may be hard to get. In the beginning of June, up to 150 species should be possible.
The Oostvaardersplassen are your only chance for White-tailed Sea-Eagle, but expect them to be two miles off at least! However, the fringes of the reserve are overrun with birders, who will help you locate it. Other interesting birds possible include Eurasian Spoonbill, Bearded Reedling, Bluethroat and Penduline Tit.
Interesting places at that time of year are:
- relict lowland peat marshes (Purple Heron, Savi's Warbler, and possibly Great Reed-Warbler): Nieuwkoopse Plassen, Naardermeer and Zouweboezem.
- late migrant waders are possible at the Lauwersmeer in the north of the country (Ezumakeeg is the best spot to try).
- the island of Texel (Spoonbill, breeding waders, terns, Eider, Common Nightingale)
- the southwestern estuaries (breeding waders, terns)
- various moorland areas, especially in the northeast of the country (Red-backed Shrike at the Bargerveen, the (still) only Dutch breeding Common Crane at the Fochteloërveen, Black Grouse possible at the Holterberg)
For Limburg in the southeast (e.g. breeding Eurasian Eagle Owl and Middle Spotted Woodpecker), June is not the easiest month.
European Nightjar is possible in many locations in the south and east, but local knowledge is helpful.
If you'd like more detailed information, send me a pm and I'll see what I can do!