Hi Arun: Your best/safest bet would be to drive down to UB from Ulan-Ude in Russia, then explore as far west as Kharkhorin and perhaps even the Tsetserleg/White Lake area and then retrace your route back out of Mongolia to Ulan-Ude. That keeps you all on sealed roads and some decent dirty roads (Kharkhorin-Tsetserleg-White Lake).

If you are determined to exit Mongolia to the west, it can be done in a saloon car if you are willing to drive very slowly and carefully. You should take the "southern route" because the northern route has worse roads and more rain, which means more mud and deeper streams to cross. You can find info on the routes on this site with some searching. You will be on dirt roads and tracks 95% of the time. Mostly OK but with some rough areas. Mongolians do drive saloon cars across those roads so it's possible. You just have to be willing to take it very easy on the speed. There are places you can go 60-80 Kph, but in other places you might have to go 5-15 kph for long periods. If it rains heavily you might have to wait a few days for the mud to dry. But it does not rain heavily very often.

I know it can be done because a German couple did it a few years ago in a tuk tuk (3-wheel Thai scooter-thing) with very little ground clearance and very little traction.

June should be OK. You should not attempt it in the cold months (October-April) because if it snows you will get stuck without 4WD.

Hope this helps.

Scott