Park Güell – The park is divided into two areas: The Forest Zone and the Monumental Zone. The Forest Zone is free and offers nice viewpoints overlooking Barcelona.
Take a Free Walking Tour with a local company – Runner Bean Tours offers, not one, but two different Free Tours every day, rain or shine. Both tours start at Plaça Reial at 11 am and 4.30 pm (in summer) and 11 am (in winter) and last for approximately 2.5 hours.
Enjoy some time at a museum – most of the public museums offer a free entrance on the first Sunday of each month and every Sunday after 3 pm.
City History Museum – The museum has a free entrance every Sunday from 3 pm to 8 pm and all day on the first Sunday of the month.
Picasso Museum – A fine collection of the artist’s early work and some of his own interpretations of Velazquez’s Las Meninas. Free every Thursday from 4 pm to 7 pm and the first Sunday of the month (online booking required. Tickets are only available 4 days before the date.
City History Museum (MUHBA) – The highlight is the Roman remains of Barcino five metres under street level. A must for any Roman history or archaeology enthusiast. Free every Sunday from 3 pm and the first Sunday of the month.
Frederic Marès Museum – It holds this sculptor’s private collection. Don’t miss the fascinating top floor displaying every object imaginable. Free every Sunday from 3 pm and the first Sunday of the month.
Barcelona Design Museum – A new addition to the city, this modern building holds an interesting collection as well as travelling exhibitions. Free every Sunday from 3 pm and the first Sunday of the month.
Roman city wall
You can walk around the whole perimeter of the Roman city following explanatory panels. The most spectacular parts are the city entrances at Plaça Nova at Pati Llimona Civic Center and the wall and towers at Plaça Ramon Berenguer. However, the wall is embedded all over the city. You can find it inside the buildings, like at the Mercer Hotel or in other houses along Avinyó Street.
Roman Domus
There are two Roman houses that recently opened to the public: The Domus of Sant Honorat at Carrer de la Fruita, 2 and the Domus of Avinyó at Carrer d’Avinyó, 15. The highlight of the house at Avinyó street is the well-preserved wall murals. Both have a free entrance on the first Sunday of the month from 10 am to 2 pm.
Roman necropolis
Outside the perimeter of the Roman city, at Plaça de la Vila de Madrid, an unexpected burial site was uncovered in the 1950s. A few meters under street level you can see the funeral monuments lined up on both sides of the old road that led to Barcino.
Roman aqueduct
At Plaça del Vuit de Març, the remains of the original aqueduct discovered in the 1980s are on view attached to the walls. Nearby, inside Casa de l’Ardiaca, not only can you enjoy for free its beautiful patio but you can also see the end of the line with the deposit that distributed water to the whole city.
Temple of Augustus
For sure you are not expecting to find the remains of a 2,000-year-old temple stuck inside a house. But anything is possible in Barcelona. At the highest point of the Roman City (Carrer del Paradís, 10), after entering the house, four impressive columns are waiting for you. This is what is left of the original temple dedicated to Emperor Augustus, the founder of the city.
Source https://runnerbeantours.com/free-things-to-do-in-barcelona
La Cova Fumada – This is by no means a fancy restaurant – and it doesn’t try to be! La Cova Fumada is a real local’s haunt which is full to the brim every weekday lunchtime.
Sésamo – This edgy vegetarian restaurant in the Raval offers a seven-course tasting menu with two drinks and water for just €25 per person.
Mosquito – Mosquito is one of Barcelona’s best gems: an authentic Asian restaurant with a wide selection of craft beers served in a cool locale in the Born.
Kiosco – If there seems to be a gourmet burger joint on every street corner in Barcelona these days, the city has Kiosco to thank for setting the trend.
Elisabets – Elisabets is a good old fashioned tapas bar open from morning to night, serving breakfast, lunch and dinner.
Chen Ji – Chen Ji stands out as the best – and arguably most authentic – Chinese restaurant in the city.
Caravelle – Casual, cool and cozy, Caravelle is a great place for budget-friendly home-cooked food that ticks all the right boxes.
Source: https://theculturetrip.com/europe/spain/articles/the-best-budget-restaurants-in-barcelona/
Metro – You can either purchase a single ticket (€2.20) or a 10-journey ticket (€10.20). And if you want to ride the metro multiple times for consecutive days, check out the Hola BCN Tourist Travel Card (unlimited metro rides on Barcelona’s public transportation system for consecutive days).
Rent a bike – Join Fat Tire Tours or Steel Donkey Bike Tour for guided tours or, if you’d rather rent a bike, you can choose from: Barcelona Rent a Bike, Green Bikes or Born Bike.
Rent a scooter – If you’re feeling adventurous, blend in with local Barcelonians and rent a Vespa to get the most out of your day I the city. Fast, easy, and accessible. Prices start from 20 EUR per hour, and you can get a discount for a full-day rent.