If I cast the banishment spell on myself while in a demiplane, where exactly do I exit?
Do I exit on my last position on my native plane, a random spot in my native plane, or do I choose where I exit in my native plane?
Jeremy Crawford has elaborated on this exact scenario:
If you cast banishment on yourself on a plane you're not native to & you fail the save, you return to your home plane. Who knows where! #DnD
When a spell effect is vague or unclear it falls to the DM to adjudicate the results. That is part of the 5e design ethos.
In this case banishment provides no guidance for the placement of a creature ejected from the plane that they are currently occupying, so it is entirely up to your DM.
In this case, you better hope your DM is in a good mood and at least puts you on dry land!
It is worth noting that nothing in the rules allows one to purposely fail a saving throw. So, your DM would not be breaking any rules in ruling you'd have to roll and fail the save for this to take effect. However it is very reasonable for DM to not rule that way.
See this Q&A for more discussion on the matter.
If the target is native to a different plane of existence that the one you're on, the target is banished with a faint popping noise, returning to its home plane. If the spell ends before 1 minute has passed, the target reappears in the space it left or in the nearest unoccupied space if that space is occupied. Otherwise, the target doesn't return.
Since the spell does not say that the caster chooses the destination, it is extremely unlikely that the caster gets to do so. Such a ruling would infringe heavily on higher level spells meant for inter-planar travel.
The spell does not explain how to determine the target's destination, so the DM has free reign to place the target anywhere in it's home plane.
However, the caster (which is also the target in this scenario) has a minute to decide whether they want to stay at the destination or end concentration to return to the previous location.
Purely my opinion, but this would be one of the many occasions I rely on a random 1d20 roll as a DM. High is good (known part of world/on or near ground level,) low is bad (Unknown location/Miles out to sea and underwater.)
Upon further review, the spell makes the target INCAPACITATED, which is a condition that immediately ends spell concentration, so by the rules, self banishment is impossible. Though you could have an ally cast it on you.