First of all, the English sentence is wrong. You probably mean: I'm going to the university today. Please note, your sentence refers to someone who works there, not a student. I'm going to the university today = 我今天去大學的。 You might want to ask in the original Russian to avoid misunderstanding.

"I’ll go to the university today" 「我今天去大學。」will be regarded as "I went to the university today." 「我今天會到大學校區去。」 is better. The future tense ─"will"─ could be expressed as 「會...」or「要...」or「將...」in a Chinese sentence. For reference only. I wish it could help.

“我今天去大学”it means "I go to university today." "will" it means “将要/将会”in Chinese. So ， I’ll go to the university today.=我今天将会去大学。

It can translate into two ways 1、我今天要去上大学了。means you will begin the College Life today,begin to study in college. 2、我今天要到大学（校园）去。means you just go to the campus,just get to a place.

“我今天要去上大学”，不过还是说的不通