We're in So Cal and got a huge discount for a date in January. Odds are the weather will still be great (and there is an excellent on-site back-up plan), but January just isn't as popular, so it saved us a third off the venue (ceremony & reception location, food, beverage, etc.) cost.
This will change from venue to venue. Gotta check with them! At my venue, April was the last month of the off season, but at another I toured it was the first month of the on season. I got married the last day in April so I chose the venue with off season pricing.
I'm in the Dallas area. The venues I went to, most off-peak is December-February and some have November, but it's getting more popular, and others go til march, but April is popular so it's normally a peak month.
We looked at outdoor ceremony, indoor reception venues.
Either way, you might consider the Japanese Gardens or Joe T Garcia's. At the gardens (attached to the Botanic Gardens), there are many gorgeous decks you can rent -- my dad actually got married there just a couple of years ago and it was gorgeous and the pictures were lovely. I don't know if they do ceremonies at Joe T's, but they have absolutely lovely outdoor reception areas that can be very private and nice.
Off-season in my area is November to March. I think April may be too late for off-season pricing but you will need to talk to your various vendors because they may have a different standard that they follow for off-season pricing.