As someone who attended a mid range state school, this is the advice I would give myself which are seven key ways to leverage the experience of a top tier university by building your own education at a lower tier university:
Do projects outside the classroom. Tinker. This will help build your calling card once you graduate, but also challenge you in the ways your classroom may not. (Remember this is one of the areas MIT excels)
Join the honors program. This feedback loop & community of peers can help turbo-charge your learning experience. It will probably make your overall social experience more enjoyable as well. This is huge. This means you get daily exposure to smart, smart people. If you can't get into the honors program or already are--you might even seek out academically based groups which aren't per se specific to your major.
Join campus groups in your interests & passion and be an active participant in those which bring you the most joy. The difference between just attending and being an active participant is easily 3x to 5x and sometimes as much as 10x. Capitalize on experiential learning experiences and other opportunities to engage in student based competitions. Its fun way to learn, it will build your portfolio, and perhaps even your circle of friends.
Tinker and create projects which you are passionate about. Collaborate with peers learning. This feedback is critical.
Seek out expertise beyond your professors (whether academic or professional)
Seek out online learning opportunities. Be willing to pay for those which will bring value.
Create personal relationships with professors. Also ask them how to optimize your university experience for your learning and career goals.
Remember group activities is often where your initial network will come from, so that important to your learning experience in college as well as later on in life.
Nathan Ketsdever, education start up researcher for past 7 years.