To keep amused
amuse, divert, cheer, please, interest, enliven, delight, beguile, regale, engross, occupy, enthrall, charm, captivate, recreate, inspire, inspirit, stimulate, exhilarate, gratify, satisfy, humor, distract, indulge, solace, relax, make merry, disport, comfort, put in good humor, elate, gladden, tickle.
Antonyms tire, bore*, weary, depress.
To act as host or hostess
receive, invite, treat, regale, recreate, gratify, feed, wine and dine, host, chaperon, give a party, have people over, have company, be at home, keep open house, do the honors, welcome, give a warm reception, make welcome, show hospitality to, receive with open arms, roll out the red carpet, kill the fatted calf, throw a party*.
Antonyms neglect, ignore, banish.