Does the space get full sun or other light? That can make a big difference in choices.

bostedo, it really doesn't get a lot of sun, maybe 6 full hours for parts of it, other areas hardly any at all. My backyard neighbors have some trees that block that side and my next door neighbor's house is huge, the sun rises and sets from one corner of my house to the other corner.

Jinx, thank you! I'll do some research on those, I haven't seen those on other sites before. Usually boxwood is most recommended or some flowering plant that will be dead half the year.

Christina, Two tropical-ish evergreen plants that did fine for us in partial Houston sun with little maintenance were Aralia (Fatsia japonica) and Aucuba (Aucuba japonica). Female Aucubas produce red berries and the male plants tend to grow a bit more upright. Won't be able to tell the gender on most nursery stock unless you catch them in flower or go with a fruiting vegetatively reproduced cultivar like 'Rozannie'. While they'll work in heavy shade, they do better/grow faster with some sun.... amount depends on the time of day; a short time in direct afternoon sun can fry them, though have seen them do well ~6 hours of morning light or dappled shade - they'll let you know pretty fast if unhappy with the light.

We didn't grow these in Houston, but might be worth considering: ‘Edward Goucher’ Abelia stays semi-evergreen in Dallas, so should remain dense enough for privacy in Houston. Works in sun through partial shade. Mexican orange blossom (Choisya ternata) may work well depending upon whether you're in the clay or piney woods parts of Houston. It will work in clay, but much more sensitive about site drainage (and pH?). 'Sunshine' is a slightly smaller cultivar.

Doubt Firespike (Odontonema strictum) will remain evergreen most years even in Houston. But mention because it does provide a tropical look, grows fairly quickly, and is easy to propagate from cuttings for a fence line hedge.

Ooo thank you bostedo! I need to wake uo early and record exactly how much sun different areas of my house gets. I think I like Aucuba (Aucuba japonica) the most. It's like a bush/vine. I didn't want anything to grow too round but I didn't want to deal with vines, this seems like a happy medium.

A great day to check this as it's our summer solstice. Sun begins its return south from now. Our Gold Dust Aucubas are planted along the north wall of our house where today they'll get the most direct light of the year before they begin to fall back under the shadow of the roof overhang again.

Aucuba cuttings root readily in water, so easy to propagate for experimenting with different sites if you have that sort of time and interest.

This is my yard at 7:30pm. The back fence area gets no sun, it did in the winter because that neighbor's tree had no leaves but it's been progressively filling in and growing onto my side so I'll have to trim it, on the left side I have my cactus and my stromanthe, the sun is there from about 11am until 6-7 but it's mainly in that corner area and not towards the back of the fence. I'll take a pic again in the morning. Thank you!

Ugh, woke up late but this is it at 11am