Seeking a a great value Barcelona Hotel around $100 close to port and city transportation

Book the first available entry time for Sagrada Familia (Gaudi)
Metro to Diagonal for a walk down Barcelona’s majestic boulevard, Passeig de Gracia
Lunch at Cerverceria Catalana (Carrer de Mallorca, 236)
Casa Mila (Gaudi) is on the left & Casa Batllo (Gaudi) is on the right as you head down
Thru Placa de Catalunya, Barcelona’s main square and you will be at the top of the Ramblas
Walking from top to bottom you will pass La Boqueria markets on the right
Left side thru the Gothic Quarter to the Cathedral. Further along to Placa Reial on the left side
Finally you will reach the port and the column with Christopher Columbus gesturing atop
Dinner at Cafe De L'Academia (Placa St Just, Carrer dels Lledo, 1)

I stayed at Pensio 2000. Quirky, kind of a B&B, very clean and comfortable, literally opposite the Palau de la Musica (I could see the entrance from my tiny balcony). http://www.pensio2000.com/en
Good location, owners very helpful. It's 3 flights up. The owner will take your luggage. You have to phone him. I didn't have a phone with me, but the woman in the bookshop next door kindly called for me.

Thanks to both of you for your responses. I will bring this information along!