Well, not sure what advice you are asking for. We did that once - traveled cross country from Florida to Idaho. What I remember as a big mistake was letting the pillows touch the tent walls when it was raining. Wet pillows next morning. Had to spend time at the local laundromat to dry them out. This was at the Devil's Tower CG in Wyoming.
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We've been from Ontario to Florida in a tent with 2 small kids. We had a great time but do have some advice. Make sure you have a tarp and rope big enough to cover over the tent ( essential if it's raining). Also duct tape is great for repairing small holes in the tent floor in a pinch. (we had a run in with ants one night because of a pin point hole. ) An electric pump for air matresses is always nice. The only reason we switched to a hybrid trailer was to sleep off the damp ground. We love our time in our tent!
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When we were younger (20's and 30's), we always carried a small tent, 2 fleece sleeping bags, 2 blow-up pillows, a pot, propane lantern and propane cooker in our trunk in a milk crate. We were always ready to stop and camp for the night. Our best vacation we ever took, we got to the intersection below our house, flipped a coin - heads was north, tails were south. Tails it was - we went to Jackson, Miss; New Orleans; Biloxi and Gulfport, MS; Gulf Shores, AL; and then to Pensacola, FL. We spent 3 weeks between 6 places and got home about midnight, the night before we were to go to work. It was a blast!!
Now we have a 33' bunkhouse because we have 2 small daughters (7 and 4) and I am old enough to really like the comfort of my own bed, even when we are on the road.
We have spent 2 weeks at the beach in a tent and we did have blow up mattresses and a large fan.
You don't say whether you have any experience tent camping. If you do not, you would be much better off IMO doing some practice first. With some experience you can do what you want and enjoy the trip - remember weather is not your friend in a tent. Staying warm and dry are the keys.
DW and I (we were much, much younger) sold a business one time and, with nothing to do and no kiddies to worry about yet, took a motorcycle camping trip that ended up lasting about 8 weeks - we had no destination in mind. We just traveled until half the money was gone and then turned around. Maybe one of the best times we had in our lives.
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I once went on a 70-day trip with spouse, a two-year-old, and a five-year-old (thank goodness in a tiny TT, not a tent) across the southern US from San Diego to Florida, up the east coast into Canada, and back sort of diagonally from Ontario to home. It rained 63 of the 70 days. There were horrible windstorms. There was heat. BUT...it was the greatest adventure of my life.
I agree with the person who says practice first if you are not experienced at tent camping. I'll also add that sleeping in the Suburban might be an option. Maybe even a motel if the weather gets too nasty.
I would opt for a class b rv or a small trailer before I would do a tent. A tent doesn't offer much protection from anything.
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