Look to the Sony PRS-T1, it runs Android 2.2 and is trivially easy to root.
https://wiki.mobileread.com/wiki/PRST...ing_and_Tweaks
Not sure about VNC (last I looked there were a whole bunch of them for Android, some free some not) but the thing looks to be compatible with a *lot* of Android apps (though not all) so you may find a match. It is early in the exploration of the device but so far people are finding a *lot* of easy tweaks.