Itinerary Help! - Portugal Honeymoon

I would suggest the Alentejo region. Evora and the small villages and fortified towns in the surrounding areas. There are cork farms, wineries and olive oil producers, as well as ceramic and marble products. Also several Neolithic sites if that is of interest. I'm going in November, and the Eastern side of the country is barely mentioned in the RS book, but after much research I can't wait to visit.

another vote for Evora. We were just there for 2 nights and we loved it! Stay within the city walls. I can highly recommend an apartment if you send me a pm.

If you were coming here at a different time of the year, I would also suggest Evora. However, at the end of August it will be extremely hot. That is the hottest part of the country and the hottest month of the year.
And, just so you will be prepared, Lagos will be very crowded during August.
Might you consider doing Porto and the Douro instead of the Algarve? The Douro is one of the big wine regions with a lot to see between Porto and the valley. Splitting your time fairly evenly between the Lisbon area and Porto/Douro would be my suggestion - especially during the hottest month of the year.

We were in Lisbon two summers ago and made a short (1+hour) side trip by bus to Sintra. We went there to see: Castle of the Moors, The Pena Palace and Quinta da Regaleira. We considered this excursion one of the highlights of our trip. Cute town with a nice mix of shops and eateries too. Although we ran out of time so didn't get to see Quinta da Regaleiria and Pena Palace was in the process of internal renovations, the Castle of the Moors was fabulous in and of itself and made the trip well worth it.

I would suggest two nights in Sintra (stayed at Sintra Bliss), arriving after 2 pm and enjoying two sights that day maybe the National Palace and Quinta da Regaleira which will be less crowded late afternoon..
Buy your tickets in advance at the TI either at the train station or in town for all the sights you definitely want to see... Taxi up to the entrance(10e) to the Pena Palace before the bus loads arrive around 9 am and stand in the ticket in hand line, You need to get in , go directly to the gift shop on the right and buy a 3 euro shuttle ticket to get to the palace ( or hire a local guide and get there early)..
This palace is outstanding and so different and unique outside and in, and well worth the stay in that little town.. take a night from Lisbon! Next the Moorish Castle wall walking...
What a beautiful place for a honeymoon stop!
August is the busiest month according to the locals I spoke with this past week. I had two of my best dinners at the RS recommended restaurants in Sintra; Cafe da Villa & Apeadeiro. Also get the ginjinha shots in edible chocolate cups as you walk around the little town.
I am a Porto fan as well, much more cosy, welcoming feel than Lisbon. I found better food at less cost than Lisbon. If you like Port wine ( not a fan, did two separate port lodge tastings on two visits), but my visit by train to the Douro Valley-Pinhao day trip as suggested by RS was the best red wine ever at Quinta do Bomfim, Symington Family Estates just to the right of the train station up maybe 3 blocks.
Unique foods in Porto too, francesinha at cafe Santiago, Cachorro Especial at Cervejaria Gazela (the one next to the national theater , they have a new bigger one two blocks away that’s always busy).
Spent one overnight in Evora which was OK, glad I went, would not return.
Use the CP- Comboios de Portugal to get train information about the duration of getting from point A to B to help you decisions on travel.

One last thing, upon arrival to Porto & Lisbon I had booked with AirBNB Experiences for my walking city tours to learn the city and get restaurants suggestions. FYI my RS was off on some prices in my book, higher at times.
Enjoy Portugal

We were in Portugal in April. Spent time in Sintra, Coimbra, Porto and Lisbon, and a few points in between. Did not make it to Lagos or other points South of Lisbon.
If you are set on Lagos and Lisbon, I would consider spending the extra 3 nights in Sintra as suggested in another reply. Sintra will be PACKED during the day, but clears out a bit at night. Plenty of sights there for two full days. Do NOT take a car to Sintra as access to driving in town was limited to residents only when we were there. We stayed at Sintra 1012 Boutique Guesthouse right near the center. Good accommodation and pleasant hosts. We hired a local taxi service for a full day (at a very reasonable price) to take us to many of the sights and tour the area. Guesthouse can give you contact info for the driver.
We also loved Porto, but it is a long way from Lagos. Might consider Porto in instead of Lagos, but that is your choice.
K