Basing near Universal Studios Japan
If USJ is the centrepiece of the trip, staying in Konohana ward near Universal City Station cuts out a daily commute with tired kids in tow, and several hotels here are built specifically around early park access. The trade-off is distance from the rest of the city — Dotonbori and Osaka Castle are a proper trip from here, not a quick hop.
Basing centrally and day-tripping to USJ
Staying in Umeda, Namba or Tennoji instead keeps the rest of the city's sights, restaurants and the subway network close, with USJ treated as a single dedicated day out via a direct JR connection. For families splitting time between the park and everything else, this usually works out more efficient overall despite the daily commute.
Room size, realistically
Standard Japanese hotel rooms run small by international standards, and a family of four in a single Osaka hotel room is often a tighter fit than it would be elsewhere. Look specifically for family or connecting-room options rather than assuming a 'double' will comfortably stretch to fit everyone.