There are several synonyms for "giving the center of the stage to" that can be used in different contexts. Some good options include "putting the spotlight on," "highlighting," "showcasing," "centering on," "focusing on," "bringing into focus," "emphasizing," "foregrounding," and "drawing attention to." These synonyms can be used in various situations, such as in an art exhibition, a public speaking event, or a theatrical performance. Using these synonyms can add variety to your writing or speaking, and make your language more engaging and interesting for the audience.