http://www.kiralyikastely.hu/index.php?mid=122 and this is the official site in english with a short history.
She visited Buda in 1751 and said yes to the invitation of Grassalkovich Antal to visit his only few year old palace in Gödöllő.
In the palace on the tour you can hear the entire story. I used as a resource this website
To get to the palace you should take to HÉV till the station called Gödöllő: Szabadság tér (Gödöllő Liberty Square). Here is a nice picture showing the mostly known sightseeings in Gödöllő.
It's a work by Márvány Miklós. There is an underpass to cross the street after getting down the HÉV or as you can see on this picture crosswalks too.
Did you know that the only original Baroque style theater is in the palace? The other two in Europe are reconstructions made by this theater. The Palace was the housing to the soviet soldiers who made a lots of damage but now it looks great. If you take the time to visit please make the whole tour its amazing i swear. Sadly when i visited i didn't bring my camera, but it's something really big. For example there is a silk dress and they renovate it all the time as they used to back then. Did you know that back then 2 maid worked on these dresses and they changed spear to spear and one maid only could change 15 spear per day otherwise they would got crazy. And there is also some big things to see which they want to buy to Schönburg but Gödöllő won't sell it.
I translate you the map:
1. Royal Castle of Gödöllő 1741
2. Baroque theater
3. Park of the Castle - Orangery
4. Royal Waiting Room
5. Evolutionary Special Museum of Agrarian Tools and Mechanichs
6. Lower Park- World Tree
7. Barrack of sergeants
8. Hamvai- kuria - City Museum of Gödöllő 1662
9. Statue of Török Ignác
10. Petőfi Statue
11. Evangelical Church 1931
12. Reformed church 1745
13. Artists' place of Gödöllő
14. Park of Elisabeth
15. Statue of Elisabeth
17. Chapel of the Castle
18. Community Centre
19. 1st War Memorial 1931.
20. Mary-column 1749
21. Premontrei Church
22. Statue of Kálmán prince 1931
23. Statue of Saint Imre 1931
24. Baroque House - Castlegarden restaurant
25. Saint Stephan University
26. Old town hall
27. Town hall
28. Police station
29. Bus station
30. Apiary Museum
31. Silver Club (it's a hotel or something, i don't know why is it on the map, but there it is)
32. Máriabesnyő (famous catholic church)
Sorry i cant give you a map like i did about Mogyoród, but here is a link from where you can print the important parts. http://www.terkepcentrum.hu/index.asp?go=map&mid=13&tid=32559&verzio=2008