You can see the dunes quite easily from the main road - take the road out to Hatta and you run right next to dunes, which are spectacular as the sun sets. You can park your car, get out and haul yourself up a dune.
Another good place for them would be in the Al Khatim area of Abu Dhabi and again, park up and walk a couple of hundred meters.
To get the true experience of being in the desert, then you need to go off-road - Liwa is simply magnificant, as is Sweihan, Al Khazna, Al Khatim etc, but you will need to do this with other people and you need to be with someone who has experience of driving in the sand.
At the moment, the sand is super soft and its very easy to get stuck. Its also very easy to get lost, so you need the proper equipment, the right car, the necessary tools for navigation and at least two other cars/4x4's just in case.
Never travel into the desert on your own. Its just not worth the risk.
The tours are okay and I have heard good things about Arabian Adventures. about 8 years ago