Our house is less than 10 years old and the builders put the hot water heater on the second floor, outside the bedrooms. It was past it's original warranty, so we decided to replace it before we moved in, just to avoid the flood and inconvenience.
My DS and BIL had an electric tankless water heater installed when they built their house. The contractor put the unit in the crawl space, so any adjustments needed after a power outage means he has to go under the house. Stinks when the weather's bad. You can set the default temperature to whatever you want, but a power outage resets it to the factory default. We're fine with the default 120°F setting, so it hasn't been a problem for us as yet.
We chose a gas tankless heater that was installed by the gas company, so both an electrician and a plumber were required. It mounted on a wall and required an air vent, so that meant putting it on an outside wall and having the vent installed. If you chose to put it in your basement, it would be installed off the floor, but the vent might mean putting a hole through the foundation, depending on what your house looks like.
We put ours in the first-floor laundry room for a few reasons. We wanted it accessible if we did need to reset anything. The vent looks fine since it's next to the dryer vent outside. The laundry room already had a natural gas dryer, so no need to run more pipes. The hot water line was easily tapped from that spot to service the whole house. It's close to the house water main, should anything go wrong.
We only have two complaints: the water pressure in the master bath isn't great, probably because the shower is the last fixture on the water line. My next-door neighbor (same style house) has the same layout and complaint with a traditional water heater, so it's probably just a plumbing design flaw. The gas company crew did offer to install a water pump to increase the pressure through the pipes. It's not that bad, so we didn't price the pump. Bought a pressure-increasing shower head instead for $40.
When it kicks on, the heater makes a little noise. Not really loud, but enough that we know when someone's taking a shower upstairs. Of course, it shuts off as soon as the water stops being used. We can close the door and hear nothing, so it's not a show-stopper.
In a way, the noise is a good thing: I'm more aware of when I'm using hot water, especially at the kitchen sink. I've stopped leaving the faucet set for the "hot" side because the sound made me realize I was wasting energy heating water just to rinse out cat food cans. That's a good thing, right?
You might want to see if there are any rebates worth waiting for, if you can hold off. I think every Lennai tankless heater qualifies for rebates when they're being offered. (We NEVER time it right, so do as I suggest, not as I do, lol.)