Arrival
The only commercial airport on the island is Honolulu airport, with code HNL. Remember to book with an American flag carrier if you want your airfare to be reimbursed by the NSF!
Several companies (e.g. Robert’s http://www.robertshawaii.com/transportation/airport-shuttle) run shuttles to hotels in the Waikiki area direct from the airport. Taxis are usually easily available, and should cost a little under $40 to get to Waikiki or campus. The most economical option is to take the city bus, but you cannot use this with much luggage.
Accommodation
The two most common hotels for math department visitors are the New Otani http://www.kaimana.com/ and the Ala Moana http://www.outrigger.com/hotels-resorts/hawaiian-islands/oahu-waikiki/ala-moana-hotel/overview. At the time of writing, these were either expensive or mainly booked up, but may be worth checking.
Most tourist accommodation (as well as a lot of restaurants, bars etc.) is located in Waikiki, which is on the coast about two kilometers from the university. It’s probably easiest to find hotels through websites like hotels.com, priceline.com, expedia.com, travelocity.com, — at time of writing, there were a lot of options available through all of these (and others). There are also many private apartments available for rent, which may be a better option if you are part of a group: you can try to find these through websites like vrbo.com and airbnb.com. The maximum NSF will reimburse for accommodation is $177 per night.
Getting around
Depending on the weather, the bus is usually the best way to get between campus and Waikiki or other parts of the city. Tickets are bought on the bus, and cost $2.50 (no change given). Schedules can be found at thebus.org (which also has real time information), although google maps is usually better for route planning.
Car rental is available from the usual companies. Hiring a car is a good idea if you want to get out of the city (although the bus does cover most of the island), but be aware that parking at hotels and on campus can be difficult or expensive.