A nuclear reactor could be located near the base; buried, as in Kim Stanley Robinson's "Red Mars". Then, a route could be selected that passed close to or right by selected investigatory sites. A means could be selected to pass current from the reactor to the vehicle as it went along the main route, providing electricity for quite rapid, but safe propulsion, while at the same time giving the rover's batteries a full charge.
When the rover reached an exit point along the main route, the crew would simply go on internal power and complete their mission, returning to the main route to return to base.
It seems to me the size and/or number of batteries would be much less a limiting factor than relying on solar power. A vehicle could be created that would easily transport a crew of 3 or 4 plus a generous equipment and supply list for extended missions, and do it at a fairly high speed, at least on the portion travelled on the main prepared, electrified road.
A series of these electrified roads could be created to satisfy any mission requirement. A series of auxiliary nuclear power plants could also be placed along these roads to insure safety through redundancy, and also to power outposts.
The selection of buried nuclear power plants is a natural. With millions of watts available and reliable, everything becomes much easier.
As an aside, wouldn't it be a great idea to turn Kim Stanley Robinson's trilogy into 3 major motion pictures at the time we are getting ready to really launch into the program. KSR would love the idea, I think, and the pictures would help drum up worldwide support for and interest in the program.
In closing, while I loved "The Martian" and other films about going to Mars, they all involve a catastrophe of sorts and the struggle to repair the damage and get back to earth. The actual program would likely involve landing several payloads ahead of humans and extensive use of robotics before our arrival to do site prep, drilling for water, excavation and tunneling and some construction. The actual arrival on Mars would be almost routine were it not for the extraordinary hopes and emotions tied to the event.
Of course, probably there will be one, maybe two, "single event" landings, successful or not, preceding the above event, but the slow, complete approach is the best, I think.