Great question! Lots of factors come into play when trying to find the right job post-graduation. Location, compensation, job responsibilities, career path, company culture are all driving forces behind what attract people to a job.
I'd recommend doing research on companies located in the places you could see yourself working in. For example, if Houston is a city you'd like to work in - find highly rated companies using LinkedIn or Glassdoor where you can see if they're hiring employees specializing in your area of interest.
Further, think about what kind of work you'd like to do - was there a class you enjoyed/thrived in that specialized in a particular industry and/or area of mechanical engineering? Since you'll likely be dedicating a big portion of your day to this new job, you'd like to ideally be highly engaged, passionate, and challenged with the work you'll be performing.
You'll also have to take into consideration other factors of a job. Some companies can offer more than others in terms of salary, benefits (retirement, vacation, healthcare, etc.), work/life balance, and culture. Maybe one job pays less but has more flexibility and lower-cost benefits vs. a higher-paying job.
Once you've developed a good idea of where you'd like to work, potential job responsibilities, and the financials required to keep you afloat, tap into all the resources available to go out and find the job! Reach out to your classmates, friends, LinkedIn, career service office, search/recruiting firms, and anyone you can think of to help.
Hope this info helps!