A paragraph of “There is” and “There are” openings can make lively details arrive with the same rhythm. Before replacing words at random, find the pattern you have actually created.
Mark the first few words
Underline each sentence opening in one paragraph. Read only those beginnings, then read the whole passage again. Repetition may create an intentional beat, but it can also delay the subject every time something interesting appears.
Change the relationship, not just the synonym
“There is a cup beside the sink” might become “A chipped cup waits beside the sink.” That revision changes emphasis and introduces a particular quality; it is not automatically better in every scene. Choose the version that matches the viewpoint and tone.
Keep one repeated opening if it helps establish a pattern, then decide where breaking it would matter. Avoid making every sentence visibly different just to pass a variety test. The useful question is whether the reader hears the rhythm you intended or a habit you had not noticed.