We will be in Portugal in early May 2019 for about 17 days. We are doing a lot of research using Fodorite reports so thanks!
I have two questions right now:

1.We are looking at area of Lisbon we want to stay in. We like smaller boutique hotels but very nice ones. Everyone says Alfama is very interesting.
But would you suggest staying there or visiting one day only? Do you recommend any other area of the city especially? Any lovely interesting hotel?

2. We will be going to Evora and then to the area around Monsaraz to see a bit of the rural area in the country. Has anyone been on one of those cork-trekking days I have read about? Suggestions on where to stay in the area?

Thanks for any suggestions you can provide!
Tracy

I'd do visits to Alfama, but stay in other part of Lisbon - there are lots of good options at many price points. And uber or public transport is easy to use.
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I did a "cork trek" in the Alentejo region with Maureen Ferguson of Grape Olive Pig and it was delightful. She is a former American restaurateur who married a guy from Portugal and now lives in Lisbon (and their Alentejo farm.) She drove and we hit a couple wineries, had a smashing time. The day prior we met at the market to shop and then went to her Lisbon place to prepare a lovely lunch, Highly recommend her services!

The Alfama is busy, but then Lisbon is very busy almost any time of the year now and the cruise traffice is only making things worst, as it does at any cruise port. There is a decent selectin of boutique hotels, with more on the way. Book early to make sure you can get the place you want. Check out Santiago de Alfama, the Valverde, Almalusa Baixa/Chiado and the Heritage Avenida Liberdade. And remember, Lisbon covers seven hills, so plan on doing a lot of walking as you explore the city.

Last May, I stayed in Baixa near Rossio Square. This area is one of the few flat parts of town. It's also perhaps the most touristy but also very practical and convenient. (Alfama certainly gets plenty of tourists too.) Alfama is lovely and unique, but it is a maze of a neighborhood on a steep hill. There are buses and trams to get up there - but if you say want to go out for dinner not in Alfama and back, you've got to navigate those hills each time. (I actually waked up the hills and down numerous times from Baixa over several days to shoot photos from Alfama viewpoints at different times of the day.) Sometimes it's just more practical to stay in a flat area and not have to worry about steep hills when walking back from dinner or something.

I wouldn't call it a mistake to stay in Alfama at all, though, as long as you are aware of the landscape.

A question: Which neighborhood would be the quietest to stay in? I believe I’ve read the Alfama can be noisy at night. Light sleeper here.

I wouldn't base that on neighborhood. Most likely, any neighborhood could be noisy or quiet. Depends where you stay.

Instead, read the reviews of the place you will be staying in. Most of them mention noise if there is any. Some reviewers will suggest asking for rooms in the back by a courtyard or something.

Thanks Andrew.