I am guessing that you are heating with natural gas and currently have either a direct-water heater (which means it has its own burner separate from the furnace) or an indirect-water heater (which means it is heated from your furnace and is essentially just a heating zone on your heating system). I would suggest you look at a heat-pump hot-water tank. These are very cheap to run. Ours provides all our hot water for under $300 a year whereas our old oil-fired indirect water heater cost us over $500 a year. And that is with us paying 23c/kWh for electricity. If you live in Wellesley (just a guess from your email address) you are paying half that from the MLP, so your cost would be $150 a year. A heat-pump hot-water tank will also dehumidify your basement which is a big advantage because basements always get damp either from condensation, water leaks or rising damp. Because it takes the heat from the air in the basement, your basement will get a bit cooler, ours cooled by a few degrees F. Because of this it is better to also insulate the ceiling of the basement so that the heat from your house does not go down to your, now cooler, basement. This is very easily done by just pushing fiberglass batts in between the rafters on the ceiling of the basement. I did this and it cost me $1,000 in insulation and I installed it myself. It is saving us around $3,000 year. If you do this wear gloves, eye protection and a face mask (like your covid one) because fiberglass fibers can irritate. It is completely safe once you have installed it.
Heat pump hot water tanks can be bought from Home Depot or Lowe’s for about $2,000 and installation will probably cost you $250 each for a plumber and an electrician. Alternatively your plumber can buy it for you and install it. We bought ours from State/AO Smith (they are the same company) but there are many other manufacturers. Ours paid for itself in about 10 years on the energy bill savings. An indirect tank will cost you about $1,500 and will have no savings from your current bill. I have no experience with a tankless gas-fired hot-water heater but I am guessing that they would cost about the same as an indirect tank and are probably slightly cheaper to run than your current tank. However you get no bill savings and no dehumidification, both of which are significant benefits to me.