From Flesland Airport take the Airport bus to the City Centre and tell the driver which hotel you will stay at. Walking distances within the City Centre are quite moderate.
Tourist info is available from the visitBergen web page. Weather in April is normally quite nice, but some rain can always be expected. Bring your umbrella! (We only have 200 days with rain per year in Bergen....)
Temperatures in April can be between 5 and 20 degrees. Around 12-15 at day time is quite likely, somewhat less in the morning/evening. Bring a sweater! Updated weather info is available from yr.no