Hi hongrellans, I am an Aussie living and working in UB and have managed to take a few trips in and around the countryside over the last year and a half of being here. Where is best for you to go depends on what time of year you are coming and what your budget is?
For example Terelj is a beautiful part of Mongolia, but staying at the flash hotel out there will cost you upwards of $300 a night, and there are better ger camps throughtout Mongolia and Terelj township itself would not be the pick of them.
If you want help organising transport and accommodation here I would recommend getting in contact with a local tour company who can put together an itinerary if you give them basic guidance on budget, days available and general list of what you hope to see and do.
I have recently organised a trip for my parents in May through Ankhaa at Tour Mongolia - website: www.tourmongolia.com email: tours@tourmongolia.com Ankhaa has been very helpful and was the cheapest of three companies I contacted for the same itinerary. She also offered other ideas of what to see and do along the way to Khustai and Kharakhorum where I had requested the 2 night/3 day itinerary for. Friends of ours recommended Tour Mongolia after a recent successful trip to Khuvsgul for the ice festival and so far I have been very pleased with their professional and friendly response.
Good luck with your plans, and I hope you enjoy your trip to Mongolia.