I was just at the Garden Gate yesterday; it's GORGEOUS. And huge, so be sure to wander all around the grounds, and into the back house with the canaries and finches. A lot of pots and statuary, a tiny tiny bit of water garden stuff.
You DEFINATELY need to get to Nelson's. I was there last weekend, for their annual Garden Party, and it's, well, it's one of a kind. LOTS of water features to see, fish, garden plants, pots, doo-dads, mechanicals, and know-how.
BUT.... WATCH OUT FOR THE KATY FREEWAY (I-10)! Construction has made travel HORRIBLE. Not to mention high useage by commuters. It's normally a 20-30 minute drive for me, and, taking detours to avoid construction and highway closures, and because we ran into other construction delays, it took TWO HOURS. We werent' the only people that happened to - we heard the story over and over.
If you can go on a weekday, not around rush hour, you will be much better off. Nelson's is open 9:am - 6:pm weekdays.
The other place you may be thinking of is Lynn's Water Gardens, which is south east of town. I have n't been there, and am not good at navigating that part of town. I've heard it's OK but not great, as the guy (Lynn is a man) is just starting up, and doensn't have the grounds and installations of Nelson's. They do have nice ads, though, so I'm guessing they're coming along on their developments.
Lilipons is gone. There is a small place up in Cypress somewhere, NW of town. Old and messy, but interesting. Also, Mirror Lake Design, up I-45 off Louetta is kinda nice. No ponds, but nice grounds. That would be on your way back to Dallas.
Eats: I go for funky and full, rather than trendy. You MUST try Barnaby's, the Fairview location, in the Montrose area. They have 2 other locations within bicycling distance, but Fairview is the original and the best. Also, Star Pizza, either location, is wonderful - always voted the best pizza in town each year. Their Garden Salad is huge, and chock-full of all sorts of veggies. The Hobbit is another fun place, sort of a hole in the wall, and for a bit more refined, Baba Yega's is well known. A nicer place that has excellent service and innovate food, without being too expensive is the Backstreet Cafe. Another neighborhood hangout is the Daily Review. All these places are in the funky and hotly growing Montrose neighborhood. Really, you can't go wrong eating anywhere in the Montrose area. It's a stone's throw from the Museum District. You should be able to find menus, reviews, etc. on line.