Finishing college is only the beginning to your career and the continuousness of your SWE life. If you have the C2C membership (collegiate to career), then your first year of professional membership is paid for. A lot of companies recognize SWE and support and encourage you to go to conferences.
Professional SWE offers many resources. You can find these sources at our national SWE website. There are Learning Resources which include articles, literature reviews, podcasts, and webinars. They have conference information and replays that so you can revisit the conferences if you were not able to attend. Also, there is a career resource section.
Other advantages to staying with SWE after college are networking, professional development, and means to meet new people in new cities.