My flight will be arriving at Barcelona at 815am, and will be connecting another flight at 540pm Ryanair....

Do I have enough time for me to travel to city Plaza de Catalunya, visit Casa Batllo and Casa Mila and Sagrada Familia, then back again to airport for my flight?

If your flight lands at 08:15, on time I hope, you won't clear customs and get your luggage for up to an hour later. If you are then leaving your luggage at the airport, catching a cab into town etc. you'll be there for 9:45ish. Your 17:40 connection means that you'll have to be back at the airport for 16:00ish, leaving town at 15:30 at the latest.

You therefore have a touch under 6 hours to see the city. You could spend all of that time at the Sagrada de la Familia alone, so you need to decide what you want to see most. Rush and you'll see them all, but not in much detail.

Yes, you could see all three, but there will be lines for admission, which will affect how much time you have at each. Sagrada Familia has a line to enter and then another (wait time last August: 1 hour) to go to the top. Batllo has a guided tour, Mila an open apartment frozen in time and an exhibit on the top floor, and Sagrada Familia an extensive exhibit inside. If you wouldn't mind limiting yourself to the open apartment in the Mila and skipping the rest of the exhibits and tours, you could enjoy all three attractions. If you want to pore over the exhibits, I'd skip Mila.

One man's visiting order: Sagrada Familia, then Batllo, then Mila, Mila being worth the visit but the one of the three I could miss most bearably if it took me too long to visit the other two. If I knew I could do all three, I'd actually do Sagrada Familia last; it's the climactic finish to the trip.

As the others said, depends on the lineups.
Agree that one could skip Mila .If not enough time.
Take a taxi to SF.

and just viewing SF from the outside is pretty amamzing so maybe outside SF then the Batilo - Parc Guell is amazing too but definately go by cab.

Thanks for all the responses....

I plan on taking the airport shuttle bus and arrived at Plaza de Catalunya, then maybe go straight to Sagrada Familia first....then on my way back and take the shuttle bus again at Plaza...

BTW, any idea on the taxi fair from airport to city?

Would the shuttle bus be a better choice?

Taxi fare is around €30. It is quicker than the bus, which gives a bit more time in the City. Public transport is not just the time in transit, but the waiting time before boarding. You don't have very long in the city.

You can buy tickets for SF (entrance and lift) online, which avoids the line, but sets you to a time. You could set it for early afternoon, though, and do one casa in the morning. I think all 3 is too much in that time period.

Thanks for the online purchase tips....will do that...

Any cheap and good restaurant nearby recommendation for Tapas or any other stuff....?