看来 / 说不定: it looks as if, perhaps
【四25】【四27】固定短语 / fixed patterns
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
看来 draws a conclusion from what you see or know: "it looks as if", "apparently". It opens the clause (看来明天不会下雨了) or follows the evidence (他笑得那么开心，看来考得不错). The conclusion is fairly firm, and it is a statement, not a question.
说不定 (literally "can't say it isn't") is a guess, bolder than 可能: "it could well be, perhaps". It goes before the subject or before the verb (说不定他不来了 / 他说不定不来了). It can also be the predicate: 他来不来，还说不定。 There it needs 还 or 现在 in front of it.
The nuance: 看来 rests on a clue, 说不定 just guesses. Compare 似乎 ("seems", more written), 恐怕 (a worried guess) and 在…看来 ("in someone's view", an opinion).
Examples
看来明天不会下雨了。
Kànlái míngtiān bú huì xià yǔ le.Looks like it won't rain tomorrow.
他笑得那么开心，看来考得不错。
Tā xiào de nàme kāixīn, kànlái kǎo de búcuò.He is smiling so happily; it looks like the exam went well.
路上堵车，他说不定会迟到。
Lù shang dǔ chē, tā shuōbudìng huì chídào.With the traffic jam, he might well be late.
他今天没回我的短信，说不定手机没电了。
Tā jīntiān méi huí wǒ de duǎnxìn, shuōbudìng shǒujī méi diàn le.He hasn't answered my text today; maybe his phone is out of battery.
今年能不能去中国，现在还说不定。
Jīnnián néng bu néng qù Zhōngguó, xiànzài hái shuōbudìng.Whether we can go to China this year is still up in the air.
看来我们得早点出发，说不定路上会堵车。
Kànlái wǒmen děi zǎodiǎn chūfā, shuōbudìng lù shang huì dǔ chē.It looks like we'd better set off early; there might be a traffic jam.
Common mistakes
✗ 他会不会来说不定。 → ✓ 他会不会来还说不定。 (as a predicate, 说不定 needs 还 or 现在 in front of it).
✗ 看来他是好人吗？ → ✓ 看来他是个好人。 (看来 states a conclusion, it does not form a question).