You can get to Ibiza by plane or by ship. There are regular flights from the Spanish airports: Barcelona, Valencia, Alicante, Mallorca. From the airport of Ibiza you arrive to virtually any point of the island by public transport, or you can rent a car.
Arriving by ship is slowly, but certainly more romantically. Ships to Ibiza leave from all major Spanish ports.Approximate cost of flight from the Spanish cities to Ibiza:
Madrid - 50-70 euro
Valencia - 77-87 euro
Barselona – 68-121euro
Direct flights from London Gatwick to Ibiza are EasyJet, Flythomascook, First Choice, Monarch. British Airways flies there from Gatwick. Also Easyjet from Gatwick and Stansted to Ibiza - flies everyday.
From London you can take EasyJet to Ibiza. Generally cheap. Otherwise, get to Barcelona and fly Iberia or Spanair.
From London to Ibiza by EasyJet for pounds 42.99- 66.99 one way
Checkout the flights from Heathrow to Ibiza via Barcelona with Iberia. You may have a few hours stopover at Barcelona airport, but there is plenty to do there and your luggage goes through without you having to collect etc
There is an airport in Kent (Manston) called Kent International Airport and is about 1.5 to 2 hours drive from London (depending on traffic!) and the cost of flights are quite cheap
If you don’t mind picking up your luggage in London you can get with a bus to Gatwick airport where you can catch a cheap charter flight to Ibiza. If you can go to Barcelona there’s a new airline, which has, a 6am and a midnight flight to Ibiza for euro 15 incl.tax one way. You’d have to pick up your luggage and check it in with them.
Iberia has connections from London Heathrow via BCN or MAD or PMI and depending on the date and departure time the price is reasonable, with the comfort that your luggage goes through.
There are no direct flights from the US.
Your best options are to fly from US via Madrid or Barcelona (many flights all day from either airport).
Other options to consider would be to fly via the many cities that have charters during the summer in the U. K. or Germany.