Do you need dream points to unlock new Island of Rainbow places and for gardening space If so how many dream points do you need for each?

Yes, you do need Dream Points in order to get additional Garden Beds as well new islands. For the beds, at 900 points, it will gain you a third bed, at 2,100 points which will give you a 4th bed, 3,500 Dream Points will add a 5th bed, 10,000 Points will give you a sixth one, the 7th bed will need 20,000 points, the 8th bed needs 30,000 points, 9th bed needs 50,000 points and the 10th bed will require 100,000 points.

Provided you're using Pokémon Black and/or Pokémon White to sync to the Pokémon Dream World then you will need 2,500 Dream Points in order to access the Windswept Sky but you are also required to have beaten 4 Gyms.

The Sparkling Sea requires you needing 5,000 Dream Points as well as all 8 Gym Badges.

Provided you're using Black 2 or White to sync to the Dream World then the Pleasant Forest and Rugged Mountain will require 3,000 points and you also need to beat all 8 Gyms. The Windswept Sky and the Spooky Manor both require 1,500 points and 4 Badges.

The Icy Cave and Dream Park do not require any Dream Point requirements or Badge requirements.