Any turf grass, including zoysia, will need water once a week in the summer heat. Your only alternative(s) for full sun will be prairie grasses like wheatgrass and blue grama. If you mow those monthly they should not go to seed. The tall seed stems are what make grasses look shaggy, but the wheat grasses don't grow them very fast. Here is a picture of a mixed wheatgrass and blue grama with a touch of strawberry clover.

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Another alternative is buffalo grass. There is one variety, Turffalo, which grows the seed stems at the same speed as the grass itself. Thus as it grows it does not look shaggy like every other variety does. The seed and flower tips are brownish, though, so it's not like they are completely invisible. Turffalo also grows much more dense than the seeded varieties. Here is a picture of Turffalo.

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In that picture you can see how the Turffalo is trying to expand over the sidewalk. Other prairie grasses usually remain in place, but not this one.

I know they say that lawns need to have water once a week but the only water my lawn has ever had is rain and it's done well enough for me. I'm not too picky about that.

I think the reason the front yard is messed up is from some landscaping problems years ago. There was this huge bush blocking the front window and the whole foundation area extended into the yard some... and there was kind of ditch that ran from that to the sidewalk in front of the house...Well, my now ex-husband and I ripped out the bush (or bushes? it was just big mess of nastiness there) and made a flower bed (which didn't go as far as the previously mulched area). We also tried to level out that ditch some...and...here's the big mistake...we got this thing (from wal-mart I think) which was a seed mat basically... not sod...but this thing you unroll and it has seeds in it... I don't think we did that thing properly... Anywhere we had tried to use that to get new grass started never really got filled in...so I think the weeds took hold...I'm just finally wanting to get something in the front again. Maybe I should just find out what type of grass I have (in the non clover areas) and get more of that since it does fine without any special attention...but I was hoping to find something a little slower growing.

Maybe tomorrow I'll post a picture of what grass I currently have in the back yard.

Anyway, the main thing I was looking for was a tough, preferably slow growing grass that would be hardy in my area.

Of the pictures above, I prefer the wheatgrass...but maybe that's just because it doesn't show the seeds in the picture.

Something like in the link below would be great, but sounds too good to be true...

Here is a link that might be useful: Pearl's Premium

I don't see anything in that grass mix that would allow it to go without water.

Filling in the ditch was probably a mistake. That was there for a reason.

I agree about the seeds on the buffalo. Plus I'm allergic to buffalo grass, so I'm not getting it anytime soon.