There are numerous synonyms for the phrase 'sit here'. Other ways to express the same phrase are- 'Take a seat here', 'have a sit-down over here', 'settle down here', 'plonk yourself down here', 'make yourself comfortable over here', 'plant yourself over here', 'rest your bones here', 'park yourself here', etc. These synonyms offer a variety of options to convey the same message in more sophisticated or informal ways. The use of synonyms enriches your language and makes you a better communicator. Ultimately, the use of appropriate words can cast a lasting impression on the listener or reader.