I generally collect using a research permit, so I don't know what the legal ramifications are for amature collectors. I would certainly check before trying to transport mantis shrimp out of the state. Assuming that you can legally collect, what species you can find will depend on where you will be and whether you dive.
Gonodactylaceus mutatus was introducted into Oahu 50 years ago and is common in areas such as Kaneohe Bay. You find them in pieces of coral rubble in very shallow water. This species is slowly spreading to other islands, but is not yet common on Maui and to my knowledge has not yet made it to the Big Island.
Gonodactylellus hendersoni is a smaller, less common species that is also found in coral and coral rubble. It is usually found just subtidally. G. hendersoni is found on all of the island.
Pseudosquilla ciliata is common on most islands, You can find it usually by walking exposed sand flats at low tide. Animals come out of their burrows and hunt when the water is only a couple of inches deep - particularly on the incoming tide. You can also spot them while snorkelling in shallow water, but capture is more difficult. A four inch adult will usually have a u-shaped burrow in the sand, ofen along side or under a piece of rubble. If you spot one going into its burrow, you can stick your finger into the burrow and start pushing your way through it. Eventually you will see silt coming out of the other entrance. Put a net over the second entrance and keep pushing your finger through the burrow. When you near the end, the animal will (with luck) shoot out the entrance into the net.
Lysiosquillina maculata is fairly common in shallow bays. Often the burrow is in sand above the low tide line. They are hard to spot and even if you find one peering out of its burrow, the only way to get one out alive is to noose it or use the Polynesian method of digging another hole right next to the burrow, put your hand down the adjacent hole, bait the burrow at its entrance, and when the animal comes to the entrance, push your hand into the burrow and grab it. If you have soft hands and aren't used to handling foot long stomatopods, this is a bit risky.
Odontodactylus brevirostris is common on outer reef slopes in 30-90 feet of water. I typically find them near Makaha. They live in u-shaped burrows in coralline algae bench. They are relatively easy to spot looking out at divers, but it takes some practrice to chase them from their burrows and net them. I usually place an aquarium net over the second entrance and stick a piece of wire down the primary entrance chasing the animal out the back door and into the net. Then you have the job of transferring it from the net to a holding container. (A plastic bottle with small holes drilled in it or a heavy zip-lock bag work well.)
Echinosquilla guernii lives in the same habitat as O. brevirostris. However, it is much more difficult to collect. They live in worm-tubes that spiral several inches down into the bench. ALso, in contrast to the other species I have mentioned, it is crepuscular and you typically only see them looking out at dusk and dawn. They do have bright eye-shine so you can spot them by shining a dive light into the hole, but then you will have to chip them out of the bench using a hammer and chisel. This can take 30 minutes or more and working at 60 feet you will be surprised how fast you can go through a tank while pounding away.
When hunting gonodactylids and odontodactylids, carry a piece of coathanger about a foot long. You can probe holes and if you get a tell-tale strike when you stick the wire into a hole, you will know someone is home and that it is worth pursuing. Nothing else strikes like a stomatopods, so you won't be fooled by snapping shrimp, etc.
Again, check state regulations before trying to collect anything - and good luck.
Roy