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Sure you can fuck in a tent in a national park. Just be quiet about it, those campgrounds aren't that big (avoid weekends). Probably would be easier doing dispersed camping on public land such as a national forest or BLM land. Depends on where you live in the US though.
Are you just looking for a car camping tent? Something from Cabelas would probably do nicely. If you want a backpacking tent Marmot, The North Face and Mountain Hardwear all make solid, affordable tents.