Take advantage of every opportunity: One favourite of many travellers who want to get the feel of the pulse of a place is setting aside time to indulge through observation and "watch a lifestreaming movie" as it unfolds right before you. You could do this by spending a few hours sitting at a park or at a favourite spot in the middle/outskirts of a city or town, whatever your destination.
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The human interactions, the smells, the sounds the colours - all that is around will leave you in the sense of meditation, and you will be sure to notice stuff that will give you lasting memories of your destination for a long time.
Get out of your comfort zone: Whenever you have an opportunity to do something adventurous get out of your comfort zone. Challenge yourself to try out things that you never thought you could do such as zip-lining, skydiving, bungee jumping, water rafting, snorkelling, rock climbing, and hiking.