Lake Balaton is a very beautiful part of Hungary and is still relatively unspoilt. The lake is very large but only averages about 10 feet deep and is fed by underground springs, not rivers. It is a very popular area with locals and Germans and in July and August is extremely busy. Outside those times it is a lot quieter. There are horse riding stables and hot spa resorts as well as the usul activities such as sailing and swimming.
There are many campsites and they range from good to...well not really too good, but if you have your own facilities then not really a problem.
Children are still allowed to play freely and crime is rare, although I am sure the odd bag snatch will occur if you are careless.
Many people state the west side of the lake is prettier and less crowded but then again, there is plenty of choice both sides.
It seems a long way away but Budapest is only 800 miles from Amsterdam so not that bad. You will be waved through at the border, and next year they join Schengen so not even that. Plus in summer it is usually much warmer than the western parts of Europe. The language is impossible but English is now becoming quite common, especially aong the young. We have never had any major problems getting what we want. Tesco supermarkets are in all the big towns as well as Auchan, Cora etc. Wine is excellent and there are a lot of vineyards around Balaton.
Give it a try and maybe surprise yourself.