When you say "€250 in total" do you mean for all 6 in your party? That's about €40 per person. I don't think that will work unless you're looking for a hostel (and there are hostels that accommodate people of all ages).

If €40 per person is indeed the budget, then you are certainly not going to be staying in Old Town so that question is moot.

Here's one low budget option with various possibilities (en suite, shared bath, or apt.)

http://www.pension-elisabeth.at/engl_main.htm

I think Bardo is correct - with such a very low budget I don't know that anyplace in the Old Town will be posible - never mind the issue of where to put the van in a pedestrian zone.

We had a car and stayed directly across the river (bridge from hotel to Old Town) but not at that price point.

Check hrs.com for rates.
If you plan to stay the night from June 25th to June 26th, you will have the Austrotel Mirabellplatz within your budget (based on 3 dbl rooms, not 6 single rooms).

Mirabellplatz (square) is technically on the new town side, but a nice area with Mirabell palace opposite the hotel. And just a 5min walk to the river and bridge to the old town. Public parking garage is also at the square with a fee of around €13-15 per day.

A few minutes further away from the old town, the NH Salzburg would also be within your budget.
As both hotels exclude breakfast (or charge pretty dearly around €15), you may want to take that into account, too.

As there are not many hotels directly IN the old town, you are in no real disadvantage.

Oops! I think I will increase my budget. I did not realize that Salzburg would be that expensive. Austrotel Mirabelplatz is a good option I will look into it.

No my question again, what would be the most desirable area to stay at Salzburg for 1 night.

We stayed at the Goldene Ente in the old town. The price included an excellent breakfast. There is a reasonably priced restaurant at the hotel. Parking garage a few blocks away.If you book direct you can get a 10% Rick Steves discount.While it would be a one night splurge, the location, meals, and services cannot be beat. See tripadvisor for more photos.
http://www.ente.at/en-prices.shtml

What is desirable?

Residing in an old house on a cobblestone pedestrian street that is crowded with tourists all day and next parking 1/4 mile away?
Actually, I find that more a nuisance to get bags from car to hotel and back for just one night, than to stay 5minutes walking away from the old town where you can park your car and get easy in, easy out. BUt only you can make this decision.

For one night, I would not stay in the outskirts or further away from the city.

Go to Google maps, find Salzburg. Switch view to terrain.

You will see the old town south of river Salzach with Mönchsberg enclosing it like a crescent. That part is desirable, hard to acces by car and very expensive. You will have to double or triple your budget. Is that worth it??

On the Northern side of the Salzach you have Mirabellgarten park, Franz-Josef-Str also shaped like a crescent until it hits Kapuzinerberg. That part is also desirable, with mostly historic buildings and in easy walking distance to old town.
You will find the most exclusive hotels of Salzburg in this area, like the Sacher or Bristol.

Anything outside this area is a bit dull (exemptions exist!), esp. the area around the main station. And harder to get to the old town on foot when you have problems with that.

Further away you can find nice and green parts of Salzburg with charming B&Bs and easy to access by car and usually simple on street parking. Just definetely not in walking distance. But by what you save compared to the old town, you can shuttle yourself back and forth by van taxis as often as you wanted.

Thanks Cowboy1968! This gives me a good idea.

Because of your time limits I would bite the bullet on price and stay in the old town. The Weisses Kreuz or the Goldenen Ente are good choices. Another place that is outside the Altstadt but a nice place to stay at a lower price is the Am Moos B&B. It is about a 10 minute bus ride from the Altstadt.

I'll third the Goldenen Ente. One of the cheapest (but still quite nice) options in Old Town. We loved it. http://www.ente.at/

Also, the old town garage is very close-by €14,00 per 24h.

Honestly, I cannot understand the logic of the previous posts.
Are you seriously suggesting that OP should pay €550-600 instead of €250 to save the time of a FIVE, maybe TEN minute WALK across the river to a dozen hotels, all of them cheaper than the few available in the Old Town??
How does that have a relevant impact on the relatively short stay of OP?
The walk from the old town garage in the Mönchsberg is identical in length to the walk to the other side of the river.
I'd seriously suggest to look at a map and familiarize yourself with the correct distances before you waste a truckload of money to save yourself from walking a 1/4 mile.

You could even take a bus to the old town

We stayed in a 4star hotel (not worth a recommendation) almost across the street from Schloss Mirabell and thought the walk across the river was pleasant. There *are* some sights in this part of Salzburg as well.

We always stay in the new town area and quite enjoy leaving the masses of tourists behind. It is our first choice.

Wow, I just checked the rates for a double at the Austrotel Mirabellplatz and the website says 150 euros. That is higher than I expected from the recommendation above.