We've recently stayed at this one in Seminyak, Bali: http://www.villakubu.com/
We had one of the one bedroom villas (Villa X) and it was fabulous. I can only imagine the larger ones will be even better. The staff and service was great too. It's really spoilt me, will be demanding my own pool forever more.
Friends recently stayed at: http://www.serenevillas.com/miavilla/home.html
and loved it so much they hardly went out.
Others stayed here: http://www.coconuthomes.com/
and really rated it too.
We've just come back from Lombok but stayed in a hotel on Gili Trewangan. It has some places that sleep 4 but is not self-contained or self-catering; just a hotel: http://www.hotelombak.com/
We liked the place but the food really was a let down.
We've previously stayed at this one: http://www.quncivillas.com/
on Lombok itself. The villas at the main location are really hotel rooms and very stylish/minimalist, but we loved the hotel as it's small and the food was great. Since we went, they've built the private villas: http://www.thequnci.com/
which look fabulous and might suit your needs. I can only imagine that the high quality of service at the hotel will be exceeded at the villas.
Lombok is a lot quieter and less touristy than Bali, but Bali seems to be changing since the bombings - much more upmarket and less drunken Surf-dude (if you stay out of Kuta, which I would recommend you do!). Seminyak and Ubud seem to be the places to be.
If I can dig out the URLs that people gave me when I was looking for Bali villas, I will edit this post. I agree with you that there are many sites but not many good ones, and photos can be very deceiving!