We've vacationed with a Basenji for about 8/9 years now. Mostly in an RV, which makes it pretty easy. All of our Basenjis seem to love going someplace in the RV. They get excited when it shows up in the driveway, anxious while we load it (They seem to be afraid they'll get left behind), and happy once we're rolling. So, the simple answer is... get an RV! Just kidding.
Once on the road we tend to look for parks or fields near fuel and snack/lunch spots to walk the dogs. Sometimes baseball diamonds or football fields work well because they're sometimes fenced! We try to keep them off the asphalt especially in the heat (AZ, NM, NV, UT), which is most of the southwest US.
When camping, I prefer a larger primitive site to a smaller parking lot style site with full hook ups. Larger sites allow more outdoor space for a dog. Primitive sites are also almost always in the dirt, which means no asphalt. YAY! Dirty dog, but happy feet. I've used exercise pens and slide lines. I like slide lines better, but only while I'm outside to supervise. One line is strung between a couple of trees and is fairly taught. A second line is clipped to the first so that it can slide back and forth from one end to the other. The opposite end of the second line gets hooked to a martingale. Don't use a harness as they can back out of it. Same with a buckle collar. My B's all seem to get triggered by other dogs and critters, so I like to be near them in case they try to bolt while on a line. Jengo was fine on a line. Haven't tried with the new two yet but I will. I've also started brining Kuranda elevated dog beds so they can lay on that instead of the dirt. If I am forced to stay at a parking lot style site I tend to favor KOA. Some KOA's have a "K9 Camp", which is a fenced off area. Some even have agility equipment. The one in Vernal Utah had balance beam and a teeter totter. That was fun getting Logan to cross them. If you don't have an RV many KOA's have small cabins you can rent. Vernal had a GIANT teepee.
Camping with dogs is great because there's always someplace to hike with them. I could turn Jengo loose in several of our favorite spots. Always bring lots of water and a collapsible dog bowl. Also took him lake swimming and on boat rides. I preferred renting a pontoon, or party boat because they have a large flat carpeted deck. Again, happy toes! The smaller aluminum boats were a bit warmer on the feet, but not too bad. The big thing to watch out for is the aluminum dock. That gets really hot!
Food. I look for restaurants that have outdoor seating and that are dog friendly. We've taken Logan to several different restaurants. He did fine, though I always brought snacks, so that he didn't feel left out. Best place ever is the Cypress Inn in Carmel, CA once owned by Doris Day. They allowed Jengo to sit inside the restaurant, in a chair, at the table. One of my favorite dog vacation memories of all time. Carmel is insanely dog friendly too. There's a dog water bowl outside every shop and bowl of doggy cookies on every counter in town. The Beach down the street is also an off leash beach.
Which brings up beaches... We love to take the dogs to beaches! We look for off leash beaches that are set back far from any road. I'll usually unhook them and let them run while watching them closely. If I see another dog approaching I'll hook 'em up and steer clear. Jengo was hit n miss, Logan's ok, and Sparkle gets excited. The fun part is when we have a beach to ourselves. The absolute and genuine joyful happiness I see in every dog I've turned loose on a beach is unmistakable. I swear you can see them smiling. Logan lives to run.
Shopping. I'm not really a fan of taking my dogs in stores. In fact... I don't do it. I'm always afraid they're going to mark something. Jengo marked an end cap at Petco once. That was the last time I took a dog shopping, so I got nuthin' to say about that activity, or how to do it successfully.
Motels/Hotels/Inns... never had to do that, so nothing to offer. Sorry.
Bicycling... Now this is something I'd like to try. Again, gotta be careful with asphalt temp, but this could be fun. I'd like to get a bar that extends out a couple feet and keeps the dog away from the wheel. This could be useful on a vacation where there are no fields, beaches, trails, etc. The Sherpa Cycleash is the one I have my eye on.
Hope that helps a little. Let us know what you decide to do and how it goes!!!
... one of the smaller ones. Maybe.
Sometimes the dogs are more behaved than the children!
