Firstly - you have left it rather late - several cruises are well on the way to being sold out!! Remember this is peak school holiday season so the ships will be swarming with children [unless you choose a child-free line]. Avoid the Caribbean as it is hurricane season. Otherwise I'm afraid it is down to budget...if you can advise a ballpark figure then perhaps we could help.
Hawaii is certainly a pleasant option as even in high summer the temperature doesn't soar. You might also consider Alaska where although it is peak season there are cabins available. Norway and the North Cape is not renowned for too many children and there are several ships which are adults only although bookings are fairly well on. If you can't find what you want you can take a chance and not book until a couple of months before when special offers do appear even for that time of year.
Oh and remember the more expensive the ship the more likelihood of cabin remember the more expensive the ship the more likelihood of cabin availablility....regards Nei.
You dont say how long you would like to go for or what sort of temperature or activity you like best. personally at that time of year and if I were only going for a week, i'd prefer the med. However that's because living in Edinburgh all year I want warmer and drier weather than I get at home!. If you are not so keen on heat, the baltics can be very nice - some spectacular scenery and very interesting ports of call. I echo the comment by Aldrich and not go anywhere near the caribbean at that time of year.
In July, I would suggest a Medirerranean cruise for your first time. Your first cruise is really special and you would have to research which cruise line would be best for you.