Without question, the best thing we have done to our house is the Tankless water heater. Payback sucks, but the performance is great. Turn-key was around $2,000.
We had the gas company install it, because it requires a larger gas supply line than a conventional water heater, and I ain't screwing with no gas lines. What's really nice about these things is you can position them basically anywhere, as long as you can vent them to the outside. No more waiting 30 seconds for the hot water to get to the shower

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We went with the Rinnai unit which requires 0.4 gal/min flow rate to turn on. Set the output temp to 104 F. Our monthly gas savings is exactly what the on-line calculator predicted: $14.00. If you have kids and do several wash-loads a week, you would save more.
Plus, if you're gone for a week or two, the gas usage is ZERO, and my air compressor fits in the space freed up in the garage!!!
The Rinnai needs a 117VAC line for the electronics. Similar units from Bosch don't need AC power as the ignition is peizo, I think. Suggest you give tankless serious consideration.