Can I use my VR&E benefits at a University?

They can be, but there are a few additional steps than "just use it" like the GI Bill where you decide "I'm going to go do this and use my GI Bill for it". The 'education' would be part of your rehabilitation/training program as developed by you and your Vocational Rehabilitation Counselor* (VRC) at the VA.

The focus of VR&E is to:
● Meet the requirements for employment in the occupational objective established in the Individualized Written Rehabilitation Plan (IWRP).
● Provide incidental training, which is necessary to achieve the employment goal in the Individualized Employment Assistance Plan (IEAP).
● Provide incidental training needed to achieve the goal of an Individualized Independent Living Plan (IILP).
● Provide training services necessary to implement an Individualized Extended Evaluation Plan (IEEP).

Depending on which VR&E track* you decide to pursue will largely depend on what your goals are and will be consistent with your disability. Again, a conversation between you and your VRC. The VRC is not a road-block, but will assist you in meeting that goal and help you if there are roadblocks (for example, you want to become _________ and the program isn't available nearby, VR&E may fund your relocation; the program of study or school isn't approved by the VA, but VR&E can explore if an exception is warranted; etc.)

As MSG (Join to see) said, talk to the VA.
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* VR&E factsheet and description of the rehabilitation plan you and the VRC will develop - https://benefits.va.gov/BENEFITS/factsheets/vocrehab/UPDATED_chapter_31_factsheet.pdf
* https://www.knowva.ebenefits.va.gov/system/templates/selfservice/va_ssnew/help/customer/locale/en-US/portal/ [login to see] 01018/content/ [login to see] 42878/M28CVA1-Educational-Vocational-and-Special-Rehabilitation-Services
* VR&E tracks - https://www.va.gov/careers-employment/vocational-rehabilitation/programs/

You need to speak with the VA and your Veterans Rep at the School Registrar.

VR&E benefits can be used at any education facility that is approved by the VA. The area of training and employment focus must be mutually agreed upon by the yourself and the Counselor. You can check for approved facilities via: https://inquiry.vba.va.gov/weamspub/searchInst.do
WEAMS Public - Veterans Affairs
Web May 1, 2020 · WEAMS Public is a tool to find institutions that participate in the Yellow Ribbon Program for veterans' education benefits. You can search by name, program type, …