I've seen cases of 还 being used with adjectives and verbs like in the following examples:
还好
还可以
What connotation does 还 give in these cases?
Chinese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Chinese language. It only takes a minute to sign up.
Sign up to join this community还 is a polyphone with two pronunciations: hai2 and huan2. Your examples are using the first one.
The idea behind 还 (hai2) in these words is still; yet.
还好 = yet good = fair
还可以 = still acceptable = fair
还 (hai2) has another meaning: in addition; else, as in 还有, 还要.
The meaning backto; return mentioned in the other answer belong to the pronunciation huan2, which IMHO has nothing to do with your examples.
The most basic meaning of 还 is "back to", "return";
In your examples it means "fairly".
The connotation is that it requires a second (returning, back to start) thought to determine that it is good (还好) .
This is answered by "Moderating positive adjectives with 还 (hái)" Chinese grammar wiki. As explained there, 还 can be used to weaken positive adjectives, most commonly 好, 可以, 行, 不错. For example,
還 has a use of still, yet. This is the use in play here. It can be used more intuitively (to english speakers) for phrases like 還不定 still hard to predict or 還不錯 still correct. Note that either of these could be written in english as "not yet predictable" or "not yet incorrect" and still make sense: depending on the context and emphasis one or the other may be better.
These other phrases you've mentioned will make sense if we continue to parse them this way, they are just less inuitive to english speakers.
還好 still good aka not yet bad becomes the common translation of fair.
還可以 still can aka not yet can't becomes the common translation of okay/good enough. Note that in this case it's usually implying still can (accept it) or something similar.
This is only one use of 還 hái. There are many other uses and not all the times you encounter it may be this way, context is always key. This is definitely the most common use of 還ADJ phrases though.