In the last few years backcountry and frontcountry sites in the Canadian Rockies have been at a premium during the summer months. Many of the sites book up early in the year. Having said that sites do become available in the backcountry and frontcountry on a daily basis. This occurs as a result of cancellations or people failing to show up for reservations.
You would need to have flexibility in your schedule to show up at any given campground or trails office to see if there are openings. Since you will have a vehicle there are a number of other options. If you are planning on concentrating on the Jasper and Banff area you can stay in frontcountry campgrounds outside the park and still access many of the highlights along the Icefield Parkway between Jasper and Banff.
The area I would recommend on the Alberta side of the Rockies is off Highway 11 (David Thompson Highway). This highway intersects the Icefield Parkway. You are about 80 miles north of Banff , 45 miles north of Lake Louise , 95 miles south of Jasper and 25 miles south of the Columbia Icefields. from the intersection of Highway 11 and the Icefields Parkway. There is one provincial campground within 10 miles (east) of the junction and another about 30 miles east. Although these sites have become more popular in the last few years you still may have a better chance of obtaining a car camping site. They are basic sites with pit toilets and run about $20 US per night.
Another bonus to staying in this area is the ability to access many day and backcountry hikes that are situated on Provincial Land. None of these hikes require reservations or permits and are first class destinations. The backcountry sites are more rustic and random camping is allowed.
Many of the best day hikes in the Rockies can be accessed from this area , if you dont mind driving from 30 to 90 minutes.
About 1hr (50 miles) west of Lake Louise in BC is the town of Golden. I am unfamiliar with campsites near the town but there are a number of hotels in this town of about 4000. I dont know the pricing on Hotels , but, I would think they would be cheaper than Banff or Jasper.