Here's another vote for Vasteras, a lovely town in a beautiful Lakeland landscape. The pumps take regular credit cards and I've never been charged for landing or parking.
There is a train to Stockholm although the bus is cheaper and some say quicker!
Skavsta has good bus connections to Stockholm timed for Ryanair flights and a hotel right on the airport, but it is expensive and has friendly but deeply irritating security. In the North, Gavle is about 1 1/2 hours from Stockholm by train and (a couple of yeasrs ago) no landing charges, but no busses either.
I've stopped many times at Bromma and there's no more spectacular way to visit Stockholm than to land there. But apart from the charges which I've not bothered to investigate recently, they also have some pre-reservation nonsense for parking which means you have to pay even if you don't go. Bromma is a Swedish tragedy.
HOWEVER, By far the most convenient way to visit Stockholm is to fly on to Finland landing at the fantastic and soon to be gone Malmi airport. (Less than 3Hrs from Vasteras by PA-28). From there it's a 25 min cab ride to the harbour and the cruise ferry 'Baltic Serenade' which leaves around 5pm and arrives Stockholm around 9 the following morning, within walking distance of the Vasa. You keep your cabin for the round trip which has similar return timings, all for less than one night in a Hotel!!!
Edited to add that a nice mid way stop would be St Peter Ording EDXO, a lovely field with modest fees and a nice restaurant. But I've no idea about customs there - I always land at Texel first.
Regarding R4 ('Cornfield approach'), Texel usually have a good idea of what's going on there and will ring them up for you. I've never had a problem getting through there but I don't know anything about the exercises mentioned above and there's a first time for everything...
Last edited by Victorian; 15th Mar 2016 at 13:30.