Hello, well in Spain we are one of the most welcoming countries in the EU for LGBTQ travelers, may I suggest a lovely road trip down our Mediterranean coast. late May/early June would be the start of beach weather on our Mediterranean coast. You can fly in to Barcelona, stay for a few nights, and then head down the coast all the way to Valencia, and then fly out of Valencia.
You'll find the stretch of coastline from Barcelona to Valencia (la Costa Dorada) to be especially interesting. This area has sandy beaches, Templar castles, Roman ruins, posh beach towns, and relatively less tourists as one would find at the Costa del Sol or the French Rivera.
Some places of interest I would recommend, along your route (north to south):
Garraf - laid back beach community just south of Barcelona. Popular with locals and with good seafood restaurants. There is also here a beach house designed by none other than Antoni Gaudí!
Sitges - the quintessential posh beach town, 30 min south from Barcelona. Has multiple small sandy beaches. Known for its gay scene, Sitges also has nice historic centre lined with boutique restaurants and shops.
Poblet Royal Monastery - a UNESCO World Heritage Site and still active 12th-century Cistercian monastery. It was a fortified medieval royal residence and contains the unique hanging tombs of the old Kings of Aragon.
Tarragona - ancient seaside town with very good Roman ruins, including an amphitheater, intact aqueduct, and Praetorium Tower, was once the capital of Roman Hispania (modern-day Spain). Tarragona's medieval old town is a delight to explore too.
Castillo de Miravet - A large riverside stronghold built by the Knights Templar with commanding views of the countryside. The adjacent medieval village spills down the cliff towards the rivers. A great place to bicycle, kayak, or take a leisurely boat down the Ebro river.
Peñíscola - With its cobbled streets and whitewashed houses, the old town of Peñíscola sits on a big rock that juts out into the sea. The town is dominated by a large Knights Templar castle that looks like something out of the Crusades. Recently, Peñíscola was used as a filming location in the T.V. series Game of Thrones.
Valencia - 3rd largest city in Spain, hometown of the Paella. Known for its futuristic structures of its City of Arts and Sciences. You will find also Modernista architecture, great museums, and long stretches of beaches. Definitely good for a few nights.
Albarracín - voted the most beautiful village in Spain, picturesque Moorish fortifications surround this medieval pink-hued village. Was once the capital of it's Berber taifa kingdom, currently in the works of becoming a UNESCO World Heritage Site. A good option for a day trip from Valencia.
Palmeral de Elche - one of the largest historic palm groves in the world, dating back to the Moorish times, designated a UNESCO Site. The Palm forest is surrounded by the town of Elche, one of the oldest in Spain, with much Iberian and Hellenistic archaeology.
Hope this helps :)