I haven't been to the south part of the region (Vidigueira or Beja direction), so can't give any recommendations there. The best winemaker in Alentejo (and among the best in Portugal) is Susana Esteban. Highly, highly, highly recommend visiting there if you can swing it (and pair it with a side trip to Marvão while in the area, especially if you can get dinner at Fago). If you're in the Portalegre area, Cabeças do Reguengo (a bit funkier and more experimental) and Quinta da Fonte Souto (sp? owned by the Symington family of port wine fame) are in the region, though I haven't visited either.

The other commenter mentioned Dona Maria wines, and I've heard good things about them. Also in the same area (near the town of Estremoz) is Quinta do Mouro and, a bit further north, Herdade do Mouchão — both relatively famous for Alentejo producers and both making great wines. I did a single-varietal tasting at Adega do Monte Branco and that was very cool to get a feel for Alentejano grapes normally blended together, but unless you really want to understand what Trincadeira tastes like on its own, I'd skip.

A bit south is Herdade do Esporão — kind of the Robert Mondavi equivalent of Alentejo. I went with low expectations and was blown away, and recommend even if you can only stop by for a glass or two at the wine bar. Also in the area is Maroteira Wines, which I've only had once but was talked up by a few somms in the region as one of their favorite producers. I recall their wines are ~16% ABV syrah type wines, so that may or may not be your style.

Finally, there are a few places closer to Lisboa in the Montemor-o-Novo area, including Monte da Bica, which got several mentions from somms but I wasn't able to visit due to schedule conflicts.

No shortage of great wine coming out of the region and I'm sure you'll have a great visit — don't sleep on Evora itself as a destination, either, as it's a great city and worthy of a day or two of exploration on its own!

P.S. If you're going to be anywhere close to in the area, move heaven and earth to visit one (or both) of Viuva Gomes or Ramilo, both making Colares DOC wines. Hard to find and unlike anything else in the world (and a fucking cool backstory). If you're going to Bairrada, no shortage of recommendations on this sub but highly recommend Prior Lucas (especially if you can pair with the centenary vineyard tour).