Every single hotel I've stayed in whilst touring in Spain has been bike friendly, that must be over 100 by now.
In Seville I've used
Hotel Casona de San Andres, it's in a great location and the bike storage (a big locked cupboard
) is conveniently in the foyer/ reception. It's minutes walk from the centre and the nightlife in the Alameda de Hercules, away from most tourists and with a lovely peaceful traffic free square right outside, it also has a great roof terrace for sunbathing and drying your clothes too.
At 35 euros a room right now, it is an absolute bargain.