I know this is weird for me to be answering since I just made a post asking this same question, but I did a lot of research and so far the options I've learned are:
Best is to bunk with friend for free. More likely to work out the longer you've been at UIUC since I would say that most younger undergrads go home for the summer.
Cheap hotel. There's Extended Stay which is around $40 per night if I recall correctly. That's still pretty expensive.
Europa House. This is Private Certified Housing that costs $24 per day. I believe you need to stay at least 2 weeks though.
Storage unit and sleep wherever (libraries, Siebel, Quad, Union, ect.). Definitely the cheapest option (besides bunking with friend). If you look hard enough you can find a comment on a similar thread to this one of a couple using this method; they apparently slept in Siebel most of the time. This one could get you in trouble so I would recommend making sure you truly look like a student, keep your ID on you, put a book on your lap, and don't sleep somewhere for more than 3-4 hours straight. Also don't show up to the same spot in the same building every single day.
Hope the fine patrons of the UIUC Reddit/Facebook pages can help you out.
Your choice would obviously depend on your income/network. And I guess your level of shame about sleeping in public.