Audrey,
I think you will love the festival! Even a black thumb like me who kills any plants he comes in contact with loves this amazing display of flowers, butterflies, and other amazing creations.
The week that you will be there you should be able to enjoy moderate crowds, so I suggest you take advantage of any Extra Magic Hours opportunities that come your way, assuming you are staying in a Disney resort. Make sure to use evening hours especially, since you are traveling without kids. Why? Families with smaller children will be taking kids back to bed at night, so attractions will have shorter lines in the later evening hours.
For park opening and closing times, just check the park calendars under the "Plan" section of the website. As for Extra Magic Hours during your stay, here they are;
- March 14 - Magic Kingdom (evening)
- March 15 - Animal Kingdom (morning) / Hollywood Studios (evening)
- March 16 - Epcot (morning)
- March 17 - Animal Kingdom (evening)
- March 18 - Magic Kingdom (morning)
- March 19 - Epcot (evening)
- March 20 - Hollywood Studios (morning)
Please feel free to write me any follow-up questions!
Have a magical vacation!