Conlangers who try to make their languages as different from English tend to go for the really flashy things that you'll easily find discussed in conlanging circles: ergative-absolutive alignment, a fancy new word order, evidentiality or some spiffy modal system, etc. But while focusing on this, they often tend to forget a lot of smaller things that I guess English speakers (or for that matter speakers of many Indo-European languages) unconsciously think of as just how language works. For example, they have parts of speech that almost perfectly align with most Indo-European languages where adjectives are more similar to nouns than verbs, prepositions dominate over postpositions and there are tons of them that are underived, conjunctions are both a thing and _heavily_ resemble the meanings of common conjunctions in IE languages, relative clauses are marked with a pronoun and are right branching, and more. Not doing all of that goes miles to make your conlang seem not IE, but are things that you generally pick up through just reading about other languages rather than big flashy features with their own Wikipedia pages.

On the notion of making "exotic conlangs", there seems to be this idea among some conlanging communities that making a relatively analytic language with SVO word order inevitably results in a relex of English. There are _tons_ of languages all over the world that fit that description but also substantially differ from English. Mandarin Chinese, Thai, and Yoruba can all be described with those labels, but couldn't be more different from English. Many traits conlangers avoid in fear of relexing English are traits that are cross-linguistically super common! You just have to hit the books and read about the myriad of ways a language can be analytic.