Steve,
Set up an account for Memorial Park tee time... and good luck, but I'll note that I've historically gone out and just done walk on both before and after the renovation, but that can certainly be risky ... but starters will fill a tee time without hesitating. Note course is closed Tuesdays, yes you should take it in if possible.
As Philip mentioned, playing the Gus can be fun, and definitely a lot easier to get tee times than Memorial! Historic place... a little funky locale, but if you're flying into Hobby Airport on south side, its on the way into downtown. I haven't seen it since Baxter Spann's 2018 reno... (Baxter did previous reno of Memorial back in 1996), have heard some positives but can't confirm like Philip.
If you're flying into/out of IAH on north side, and the timing fits, you may want to consider Cypresswood, Tradition course on immediate north flank of airport off FM1960 to get a taste of convenient Houston golf. Or on a lark, head east of airport on FM1960 to play Tour 18 in Humble. which you may fly over depending on the wind direction.
You'll need a member for Carlton Woods, Fazio or Nicklaus... or Champions, or Woodlands CC (sorry I'll be out of pocket late Feb early March)...
So next question is where you're working or visiting, "greater Houston" is 40 miles N,S, E, & W from downtown center... sundown is now a little after 6 PM...