Buy for the man, not the baby, and buy something that works on the day it arrives. Anything needing assembly, a booking or a free weekend is a gift for a future version of him.
New dads get given a great deal of equipment and very little that is theirs. Everything in the house has become functional, and most of the gifts reinforce it.
The better present acknowledges the person who existed before the sleep changed.
Buy for the version of dad that is on hold
Whatever he did with his own time three months ago, he is not doing now. That is the gap worth filling, even in a small way. Good coffee at home when leaving the house is complicated. A tasting pack he can open at nine at night when the baby finally goes down.
Keep it low-effort. Anything that requires a free weekend is a gift for a future version of him, not this one.
Time is the gift, if you can give it
A voucher for a thing he likes, paired with an offer to take the baby for three hours so he can use it, is worth more than either half alone.
This is also the answer when the budget is nothing. Write it down and put a date on it, otherwise it never happens.
