Aloha Micah,
I live on the big island and at one point looked into doing something like this so let me share some findings with you.
First, @Ryan D. is correct about both the land and STVR rules.
While it is still possible to find land in the 15-30k range, there are only a few areas on the island that this is possible. In the Puna area there are many jungle lots that can be had in that range. For the sake of this discussion I will lump Volcano in with Puna as it will have many of the same problems, but is generally more visitor-friendly. And in Ocean view near the southern tip of the island there are also many lots to be had with or without utility hookups. They sit on a giant lava field and are a long ways from everywhere else, which is why the land is so cheap.
You will generally have a harder time drawing visitors to these areas, as they are distant from the more developed parts of the island and the micro-climates in these areas are less desirable (either dense rain forest or windy and barren lava fields).
And as mentioned, those areas have a bit of a reputation for being less safe, particularly for visitors (higher levels of drug use, theft, intolerance of tourists, etc.) There are safe neighborhoods in these areas though, so if you decide to move forward be sure to do your research. A bit like investing in a place like Detroit -- make sure you talk to someone with inside knowledge to know which neighborhoods are safe, and which are not.
The link that he sent is a good overview on STVR permitting in Hawaii, but in short, on the big island the only way to legally run a STVR is to purchase a house that has been grandfathered in already with the non-conforming use permit or to buy land that is resort zoned (generally much more expensive and harder to find). There are quite a few people who are still running unpermitted STVRs illegally on the island, but the county and state have been cracking down hard and you can expect to pay some hefty fines if caught.
If after all this you still want to try your luck, then you should also consider that building materials and labor costs are much higher here than on the mainland. And in order to be insurable (an absolute must if you are going to rent it out), the tiny house would need to be built on a foundation under county building codes (which are NOT friendly to tiny houses) or to be certified as an RV by the RVIA or NOAH. Either way, you are going to be hard pressed to get a unit nice enough to draw in visitors for the price points you described above.
I hate to be a buzzkill but I want you to know just what you're getting into before spending your hard-earned money.
Best of luck!
--Paul
