What is the best time of the day to visit La Sagrada Familia and Park Guell?

La Sagrada Familia = 0900. I am very serious about time. You will be one of 10,000 tourists that day.
Personally, I think 1 hour is enough. But, I just walked around and read placards. Did not visit tower.

Park Güell = 0800 for the park (free part). Not the houses (paid part).
Take the #24 bus from Plaça de Catalunya. It stops at the middle entrance to the park. It saves a lot of uphill walking. The Metro leaves a lot of uphill walking as we discovered on our first visit.

For eating: Yelp and TripAdvisor. You will at least avoid the tourist traps.

Any time of day that you have a timed ticket for Sagrada Familia (purchased well in advance) will be fine. We went at 9:30am in July. It sold out for our time slot (at least the tickets with a tower, not sure about general church admission). While it was crowded, it wasn't that bad. Very quick to get in, very orderly. We spent about 2 hours there. We had to pay for the audio guide but didn't use it (if you get a tower ticket, audioguide is included). I did not feel that I was missing out without the audioguide, but then again, I'm not a audioguide kind of person. We really, really enjoyed SF by the way. Very different than any other European church/cathedral I've been to.

I used to live in the area, and for a pretty good local favorite, close to Sant Pau, head over to Restaurant Azul on Carrer de Còrsega. You will only find locals here, however communication may be a bit of a challenge, as they probably do not speak English, and the menus are only be in Catalan/Spanish. Order from the "Menu del Dia" during lunch, for a high quality regional/seasonal menu at an amazing price!

If you were not ascending a tower I would recommend the first time-slot at La Sagrada Familia, because there would be no hold-over people in the church when you walked in. But with a tower ascent, I think you need to go line up for the tower right away, so the church will have lots of visitors when you're ready to see the lower level, no matter what time you go.

I spent about 90 minutes at La Sagrada Familia without a tower. I used the audio guide and liked it. I do find that I spend more time in churches and museums when I use an audio guide. I went to the small museum at LSF, which focuses on design/construction. I found it quite interesting and it was blessedly free of other visitors. I also spent 5 minutes or so in the shop. Be aware that once you enter the shop you cannot return to the church, so be careful about that.

I don't think LSF, Sant Pau and Parc Guell are too much for one day, but you'll be on your feet a lot. Sant Pau is a multi-building complex with nice grounds. I spent 2 hours there and had to hurry to finish before it closed. I believe an additional building has opened since my visit, so I recommend allowing longer. Meal hours in Barcelona are late, so if you book an early LSF visit you can go to Sant Pau before lunch and you won't need to worry too much about how long you spend there. Long visit? Grab a quick lunch in the area. Shorter visit? Have a leisurely, sit-down lunch. I don't think I'd book Parc Guell for before 4 or 4:30 PM, but I haven't checked the closing time. If you get there a lot earlier than your ticket time, you can go first to the free-entry area.