This is going to have the same price premium concern as CarMax, but I was very impressed by Carvana when I was browsing through their inventory and process. I didn't end up buying from them, but the shopping experience was fast, easy and transparent. I had a lot of confidence that I would have gotten a solid vehicle from them, if I was willing to pay for the premium service.
There's at least 2 thing to consider when you're talking about a reputable dealer.
The first is whether they're going to sell you a vehicle without being honest about any problems with it. There are a couple things I've done to mitigate this. One is shopping for certified used vehicles. Certified used really is a warranty that gets attached to the vehicle and at negotiation time you can get them to remove the certified label and warranty. I've done this twice and it knocks maybe $1500 off the vehicle (going from memory). Certified isn't a guarantee, but it gives me some confidence that the dealer has checked for obvious problems, accidents, damage, etc. The other thing I'd advise is getting your own mechanic to look at the vehicle. There are mobile mechanics that will come out to a dealership and do an inspection for a couple hundred bucks.
The second thing to consider regarding a reputable dealer is whether they're going to hit you with BS fees and surprises on the deal. Unless you're buying from a CarMax or Carvana, you're almost certainly going to run into this. I don't think I've ever come across a dealer that doesn't try to tack stuff on. You just have to be prepared, watch out for it, know what's fair and be ready to walk away. I like to make it easier on myself by shopping for really common vehicles so I can be honest with the dealer and tell them, "I've already found a dozen of these Honda Odysseys online that I'd be happy with. If you don't want to make this easy, I'm happy to go to the next one on my list."