Wife and I traveled for about a month, driving from CT to AZ by way of the south (furthest south we hit was Destin, FL). We were able to stay with some relatives, for free nights.

Camping ranges between 0-35 a night. At 0, you don’t get running water toilets usually. Most of the time, state parks were 20ish a night with bathrooms and showers.

Gas was the killer for us. My old Ford ranger only gets 23ish mpg on a good day. We were spending easily 50/day on gas when we were moving.

We occasionally slept in hotels, when the price was right and we just needed a recharge. They were 40-60/night. Or if we wanted to go to a city. If we did free camping, we’d hotel the next night usually to get a shower, for instance. Although showers are available in truck stops, too, I think it was like 7/shower so it’s almost cheaper to just spend money on a camp site with a shower. Occasionally you’ll find a free Campground with running water, but never shower unfortunately. Like there’s a great one near the Navajo national Monument.

Food… We would usually skip at least one meal to keep costs low, usually breakfast. Or we’d just make oatmeal with morning coffee or something. Lunch varied in prices. Cheapest was Texas, where we found sausage sandwiches at a BBQ place on the side of the road for a whopping 2.50. We would generally spend 10/person per meal though for dinner or lunch if eating out, and that’s including going to the grocery store for things like a rotisserie chicken plus sides. Tipping adds up, too.

If we cooked ourselves, we did better, but that was mostly beans and rice and lentils with few fresh meals.

Our grand total ended up being about 110/day. We didn’t do hardly any attractions, and we lived pretty minimally, but we could’ve gone more minimal. Camping wasn’t great until we hit new Mexico. It was too hot in the south (August) and too expensive in the north (30+/night).

4 months for 4-5k is possible I think, but you won’t end up really doing much imho. Definitely pickup America the beautiful Pass though, at least you’ll see the parks. Beyond that, you won’t have budget for like, Disneyland, or universal studios, and you’ll need to be quite minimalist if you want to go to cities.

New Orleans, for example, destroyed our budget for a while, and we did free walking tours, free Sazerac tour, etc. But having to eat out so frequently was expensive and staying in a hotel. We couldn’t afford to go to any music shows and we could only afford to get one traditional new Orleans meal, at mother’s. Besides that we ate tacos and street food mostly, po boys in little bodegas, and our hotel provided free water and coffee.