Everyone will have a different reason for enjoying their stay in Budapest, or, like me, for returning 4 times. I do enjoy the various art museums all over town and Parliament, the Terror House and Dohany Street synagogue for indoor activities, but also just really enjoy exploring this wonderful city on foot (and tram, bus and metro--all very easy to use). My personal things I do on each trip now include spending time on Margit sziget with the storks (island in the Danube just off Parliament), time on Castle Hill, huge flea market fan so the Ecseri piac is a must for me and I like to do a day trip to Szentendre, about 45 minutes away on the local train. I have also visited Godollo to tour the small palace there and another day trip to Tata, the town my mother's family came from. My next trip will include Pecs.
If you're there in April you should be able to catch the Spring Festival at Vorosmarty ter, unique hand-crafted items and wonderful food. https://www.budapestbylocals.com/ This website is helpful for determining what events will be going on in town when you're there.
As for lodging, 3 times I have stayed at Residence Baron near the Great Market, steps from the Danube and a very peaceful and pleasant area. Next trip they didn't have my dates so I'll be more mid-town, near the Oktagon off Andrassy. Most first time visitors will find mid-town to suit their needs perfectly.