Barcelona walks

Assuming that you will have little to no jet lag (depending on where you are coming from) I think that your general plan is pretty realistic.

Some suggestions for specific places:
In the Barri Gotic, there is a pretty good (and overlooked) history museum called the Museu historic de la ciudad de Barcelona. It houses the archaeological remains of Roman Barcelona (Barcino) together with the medieval royal palace, Plaça del Rei. The really cool part about this museum is that the Roman ruins are actually all underground. You take an elevator down to a 4,000 square meter subterranean archaeological site, directly below the Gothic Quarter!

Also to complement your Sagrada Familia visit you could also visit the Hospital Sant Pau, which is just a short walk away. Hospital Sant Pau is a Gaudi-esque modernisme complex built in the early 20th century. It has been named a UNESCO World Heritage Site and has significantly less tourists than the Sagrada Familia.

May I ask what time of year you will be visiting Barcelona?

I will be there next week, Sep 27 & 28

Ah ok... I ask only because next week September 19-24 is La Mercè which is the annual festival of the city of Barcelona. The festivities include 100s of events spread throughout Barcelona's squares, streets, museums, and parks - all for free.

Shame you will miss it by a few days, oh well... now you will have all the more reason to return next year :)

I will be traveling alone and am also looking for ideas for the evening that will be safe. Possible evening performance at Casa Batllo? and also any recommendations for a good paella restaurant. It is one of my favorite dishes.

If you are starting at Sagrada Familia (and note referring to it as just ‘Sagrada’ makes no sense at all) then follow with Casa Mila & Block of Dischord, and finish at Park Guell late in the day.

I am not sure about evening performances at Casa Batlló.
But If you like Paella may I recommend trying a Fideuà, which is like a Catalan version of a Paella, except instead of rice we use short noodles. It is getting more and more difficult to find good Paella/Fideuà places inside the city (most of the good ones I know are actually in smaller towns outside the city).

However La Barca del Salamanca, located next to the Port Olímpic, may still be good... but I am not 100% percent sure as I have not been there in several years. When we went you would only see locals there and a few of the FC Barcelona players would go there too on occasion. The restaurant had a pretty good Menu del Dia for lunch which usually included Paella and Fideuà among other things. Again the restaurant is still there but I am not sure how the food quality has hold up these past few years.

Google Maps says it's about 1-1/4 miles from La Sagrada Familia to Parc Guell. I believe the park is significantly uphill from the church, so I trust you're in good shape. You're squeezing a 4- or 5-day city into two days, so you might want to spring for a taxi rather than spending a half hour on that walk. There's also a bus (I think #92), but I don't know exactly where it stops or how frequently it runs.

You'll probably need to buy a ticket to Parc Guell in advance to avoid a long ticket line.

I will also be in Barcelona during that time. I'm planning to do La Segrada Familia and and Sant Pau on the 28th as well. I have tickets for 9am for Segrada Familia too. Small world!!