Hoge Veluwe national park is indeed a good suggestion, but this is only a small part of the bigger Veluwe area which is very green and even has some hills. :-)
In www.weekendjeweg.nl</a> you can do a search for hotels in the area called Veluwe, I am afraid it's all in Dutch though and only bookable with Dutch debit card... but you might find some interesting hotel names and photos and book through other sites. Also check www.hotelletje.nl</a>, you can search for 'romantic' or terms like that.
I was personally pleasantly surprised by the lovely countryside in the north of the Netherlands. Especially the parts north and south of a little town called Appelscha are excellent for bike rides. The big LF 9 scenic, signposted (in both directions) bike route takes you through a forest, and beautiful moorland (heath).
In the north you will find many farms and meadows full of black and white cows.
Also look into the Wadden islands. (especially damoc / poster #8!). Avoid Texel because it doesn't really give you the 'island feel' as much as the other islands do. You do need a couple of days though, it's a bit of a drive from Amsterdam and you need to take a ferry, they don't go until very late at night.
The provinces of Friesland, Groningen, Drenthe and Overijssel all have natural beauty with lakes, forests, meadows, special bird lands etc.
The city of Groningen (in the province of Groningen) is a really nice, small, studenty city, hardly ever visited by foreigners.
Zeeland is also a lovely area although the landscapes are a bit monotonous. But there are some lovely picturesque small towns like Zierikzee, Goes, Middelburg, Domburg (also look into Bommeljé Hotel) with a beautiful rough beach... and is very easy to combine with Antwerp, Ghent and Bruges.
Around Maastricht you will find a lovely hilly countryside which is excellent for walking. And for example visit the jezuit caves if you want to see something interesting. Maastricht has many nice cafes and restaurants, a medieval wall you can walk on, some retro shops, etc.
My favourite city in the Netherlands after Amsterdam is Nijmegen. It used to be a left-wing / liberal city with lots of squatters, feminist activists, gays etc. It's more bourgois nowadays but the atmosphere still lingers, and shows through the relatively big amount of arthouse cinemas, women's book shops and gay cafes. It has many great cafes and restaurants, a lovely park, amazing 2000 year old architecture and cobblestone streets, a river, and is surrounded by beautiful countryside with rivers, meadows, farms, and signposted bike routes (for example the Ooij route is a very convenient circular route that takes you on a little ferry across the river and past beautiful meadows). Near Millingen (along that Ooij route) you will find the lovely Millinger Theetuin, a tea garden. It's still open in October. You pay an entrance fee which includes a free drink. If the weather is good this is a nice place to enjoy some pie or soup on one of the various terraces or patios.
It's also very easy to get from Nijmegen to Arnhem which is another nice city, and in fact on the edge of the Veluwe green area which I mentioned above.
Near there you will also find Apeldoorn (boring city but with impressive villas) and its Apenheul, a monkey zoo where lots of monkeys roam free and may climb on top of you.
I don't know any flea markets apart from the one on Waterlooplein in Amsterdam. From what I know small villages may have a yearly or monthly flea market. The Dutch word is vlooienmarkt, this may help you find something through Google.
More tips on Amsterdam on my website.
Veel plezier!
Cécile
Amsterdam
