I'll also be landing in Madrid on 5/3, and plan to book ahead for that stay. It's nice to be able to know where you're headed, and not have to go door-to-door looking for lodging the first thing you do...
As for the other plan of not booking ahead...I've never had a problem with finding comfortable lodging on a moment's notice anywhere in Spain (including Barcelona, Granada, Burgos, Bilbao and Avilés, to name a few destinations). This is drawn from two trips' experience with two traveling companions...you may not get your first or second choice, but there always seems to be enough to go around. You may want to consider checking the holiday calendar, especially on a weekend in a popular city, to know what you'll be up against, and whether you should have a "plan B" ready in case of need. If you're traveling alone, you may have a bit of an edge...single rooms seem to be readily available in many areas.
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Ongi etorri!