We have a whole house filter that was easy to install in the basement. It filters all the water not just to the hot water dispenser.

It will depend upon your definition of "a lot of space".

There are after market, single use filters which can be installed in the sink cabinet with a dedicated HW dispenser.

We have a H&C drinking water faucet at a corner of a sink. The under the counter filter provides water to the cold water faucet as well as the under the sink instant hot water heater. Neither takes up much space in the sink base.

We love our instant hot!

Yep, you can put a filter on the in-cabinet hot dispensers (and have it filter cold too if you get the hot/cold model). We used an Insinkerator in our last remodel and it was nice.

Probably not what you had in mind, but you could get a GE Cafe french door fridge :)

That's not instant hot water, though.