I'll be arriving in Budapest on May 15--it's a lovely time of year there, and if you're around the weekend of the 19th-20th I highly recommend going to the free Festival of Museums on the grounds of the Hungarian National Museum, near the Kalvin ter exit on metro line 3. Beautiful shaded grounds, exhibits from museums all over Hungary, great (and cheap!) food and drink, crafts, music and it's full of locals. I loved it so much when I found it by accident in 2016 I planned my visit next year around it.
Since falling madly in love with Budapest in 2014 I have now visited 3 times, and each time stayed at Residence Baron--steps from the Danube, Fovam ter and 2 metro lines, tram, and the Liberty bridge and Great Market Hall. It's at the end of a pedestrianized shopping street, Vaci utca, so while pleasantly busy it's also quiet. I like this area a lot, but for next May I couldn't get my dates and will be staying mid-town at Hotel Medosz, near the Oktagon.
Keleti and Nyugati are well-served by metro lines, so just choose a place near a metro station and you'll be easily able to get around. Most first time visitors do well in a mid-town location.