One of the favourite and reasonably priced (for a major city ) Caravan Park/Camping Grounds in the ACT is at the Canberra Showgrounds/EPIC.
The camping area is large with room for big rigs.  
Pet friendly.
Grey and Black water Dump sites
Laundry
Drive through sites.
Public transport close by
Farmers Market each Saturday morning.

As at 26/5/20012 the Fees listed are:  
Powered sites $28 per night 
Unpowered sites $22 per night
(fees are based on two people, extra persons $5 each per night)
http://www.epic.act.gov.au/camping/
There is a list on the website which gives more info including a couple of dates when the EPIC’s camping facilities are closed each year eg for the Canberra Show.
In Canberra city itself many of the car parks are too low for our 4wd with roofrack, but there are some outdoor parking areas, on London Circuit.
If you are visiting Parliament House there is a large car park underground that has some spaces suitable for motor homes near the Bus parking. Probably best not to attempt to tow a rig into this Parly house car park as if it is busy then maneuvering would be difficult.

A large Woolworths is in the suburb of Dickson and is approx 5 mins drive down the Highway from EPIC. The car park (Pay Parking) is not undercover at present so height is not an issue for vehicles, but don't tow as there is insufficient room for turning for most rigs. Most who are towing would need to park in a residential street nearby.
There are future plans for undercover parking - maybe we might be lucky and the planned car park will have sufficient clearance.
Restaurants, take away etc.
Not far from Woolworths (1-2 minute  walk) is one of Canberra's very popular multicultural restaurant areas.  Two of our favourites are Bollywood Masala (Indian) and Rasa Sayang (Chinese/ Malaysian) there are a number of other cuisines to choose from so have a walk around the Woolley street area.  We are yet to try the Etheopian restaurant - Fekerte's, but will add our thoughts in due course. Many of the Dickson restaurants are listed on http://www.yourrestaurants.com.au/act/canberra/dickson/

Thanks for that Josephine and welcome to the forum.

Epic

convenient to public transport for a night out when you want to drive

site are reasonable , could be a bit more level , east west

amenities leave a lot to be desired , not cleaned everyday

few ferals

but all up probably a bare 3 star