3 nights/2 days in Barcelona

You pretty much have to prebook for the Gaudi stuff or wait hours in lineups.

Your Monday seems a bit full. We stayed near Placa de Catalunya, also. It is entirely possible to walk around Barri Gothic and then back UP Las Ramblas from the waterfront to where you are staying. We did. So consider doing both walks on Tuesday, in combination somehow.

I think an hour is plenty for Park Guell. Most of the interesting stuff is clustered near the gingerbread houses. Not sure how long it takes to get from there to the church, though, as we did things in a different order.

I'd suggest the Picasso Museum first, if you have a prebooked entry time. It's just easier, I think.

My favourite place to eat in Barcelona was Theresa Carles (recommended by Rick Steves, but we didn't realize that until we met a couple there who were on a Rick Steves tour, as it was also recommended by our Air BnB hostess). It's vegetarian food, and we're not vegetarian, but the food was so delicious, we ate there twice. It was right near our place, just off Placa de Catalunya: http://teresacarles.com

You've chosen Casa Mila and Park Guell. When we were there, we did Casa Mila, Casa Batllo, Park Guell and Sagrada Familia in one long day. If you're just choosing two of those three Gaudi spots (there's even more!) I might consider Casa Mila and Casa Batllo. I liked Casa Batllo better than Casa Mila...way cooler architectural whimsy/detail in there. Park Guell was nice but way out of the way and not nearly as cool as the two buildings.

If you're set on Park Guell, consider a cab up there. We paid 10 Euros for the cab - Metro leaves you quite a ways away from Park Guell. If you're set on public transit, the bus is better, I think. But, hey, that was a really inexpensive cab ride and very convenient.

Also, we walked back from Park Guell. Through the lovely Gracia neighborhood. 2.5 kilometers to Sagrada Familia, so quite walkable.

I would start each day with something that had to be booked in advance. Since you already booked SF for the evening, maybe move Casa Mila to Tuesday morning, you won't know until you've left it how long you'll want to be there.

IMHO, La Rambla is overrated, and you'll probably end up walking along it anyway. I think the Picasso is too, unless you are huge fans - it's mostly his very early work and his cubist period. I'd plan to do an RS walk in-between other things, so you can speed it up or skip some of it, if time runs out.

Monjuic depends on what you want to see there. The views? The museums? MNAC is much better than the Picasso (IMO of course). Depends on what you like - Miro?

I loved the Palace of Catalan Music (Palau de la Musica). You do need to book an English tour in advance. I'd recommend that over some of your other plans (though not Gaudi).

If you want to maximize sightseeing time, don't stop for long lunches, just grab something quick, and then some wine and tapas in the late afternoon or early evening. Dinner after everything else is closed, 9.30-10.00 p.m.

On Monday I would concentrate on Passeig Gracia (visit Casa Batllo or Casa Mila) before heading to Park Guell and finishing at Sagrada Familia.
On Tuesday I would walk the Ramblas, explore the Bari Gotico, and discover La Ribera, before perhaps finishing up at Barceloneta - the beach/seafront. Schedule an afternoon visIt for either Picasso Museum or Palau de la Musica Catalana.
I would leave Montjuic on this occasion given your limited time.

I just want to second almost all of Chani's points.

The Ramblas is just a street, and these days not very nice or special. If you love the Champs Elysee (Paris) or the Nevsky Prospekt (St. Petersburg), or for that matter Fifth Avenue (New York), then you may find walking it worthwhile. Otherwise, just go to the sights you want to see there (like the Boqueria Market).

For such a short time in the city, you're seeing a lot of Gaudi and none of the other Modernista architects. Since the Park Guell is out of the way, I agree with Chani that you should instead see the Palace of Catalan Music, which is fantastic. Tickets and preview here: http://www.palaumusica.cat/en/a-barcelona-mustsee-sight_151243

I can't compare Casa Mila and Casa Batllo since i only saw the latter. However, I loved Casa Batllo and spent about two hours there. Given the cost of seeing these, as well as Sagrada Familia, I'd allow plenty of time. Seeing fewer Gaudi sights and spending more time in the ones you do see minimizes both Gaudi overload and financial ruin (they add up).

Chani is also right that the National Museum of Catalunya is wonderful. I haven't been to the Picasso Museum for 20 years, but given the need to reserve, unless you have a special interest, I'd skip it in favor of something else.

Another vote for giving the Picasso Museum a pass, especially with only 2 days.