There are many varieties that would do well in your area. Brent and Becky's has great advice and has even written a book called Daffodils for North American Gardens. It is available at their site and maybe even in your local bookstore or library.

Here is a link that might be useful: Brent and Becky's Bulbs

I live right on the line between Zones 7B and 8. I adore daffodils, but it is true that many of them don't like our climate. Brent and Becky's is where I order most of mine too, though McClure and Zimmerman is good also. Here are some that I have had great luck with:
Thalia (white)
February Gold
Sweetness
Naricissus x odorus Linnaeus (Campernelle): My all time favorite, the earliest to bloom, most years in early February, and wonderfully fragrant: also fine foliage that rots away fast
Narcissus bulbocodium conspicuus (Hoop Petticoat)It's tiny, but it's oh so charming.
Hawera: a close second to Campernelle: a late bloomer and the finest textured foliage of any I grow
Peeking Tom
I have it on good authority that Grand Soleil d'Or is excellent too. I have ordered a few to try this year.

All these varieties are miniatures and species bulbs. You may think they won't make a big impact, but plant lots of them and in a few years, they will make big clumps and stop traffic.
You will find that the big trumpets, for the most part, don't do well for us. The exception would be the King Alfred Types (Carlton, St. Keverne). It's likely your Ice Follies will diminish and even disappear after a few years, but they're inexpensive and easy to replace if you love them.
The very best source for good daffodils is to find someone in your area that has lots of them and beg to dig a few at the end of the season just before the foliage disappears. Or take a ride in the country and dig some, not all: leave some to replenish what you take!, from the ditches and wild places. The ones I have gotten these ways never fail to be stalwarts in every way. While you're on the prowl, keep your eyes peeled for Atamasco lilies (a spring blooming rain lily). They bloom about the time the daffodils are declining and are absolutely fabulous bulbs. I have never seen them for sale anywhere. You can learn all about them by Google-ing them. Leucojum (Snowflakes) is great too.
For best results, feed your bulbs every fall and in very early spring.

Peeping Tom is a good one. So is Campernelle. There are several others as well now that I remember. Avalanche, Dick Wellband, Erlicheer, and Early Louisiana, Thalia, and Trevithian are suitable. So is Carlton and Geranium.

I live in TX on the 7b/8a border too! I've had food luck with the tazettas. They came back and everyone stops to look at them. Same with Avalanche and the others mentioned.

I've also gotten the Southland mixture from Van Engelen and they keep on coming back. They bulbs are so heavy you won't mind the cost of shipping....much. Last year they made it to the late November sale.

Also, Sam's has some of the same varieties only smaller.
Barret Browning, Ice Follies, Ice King, can't think of the others.

Thalia hasn't returned well for me and I've tried twice in 2 different areas of my garden and 2 different sources....darn it!

Thanks to everyone for the great advise.