Free & Easy
You don't have to spend big to get the most out of your destination. Sometimes it just takes a little bit of curiosity to uncover some hidden gems.
A lot depends on what you like to do. There's no point in going to a museum if there is nothing of interest to stimulate you, but what you can do is target activities that appeal to your interests, like phtotography, history, culture, food etc.
As with most things you can Google search for "Free activities in (wherever you are)", but make sure you add the extra interest words such as "for photographers" for "music lovers" and so on.
My own personal interest is local graffiti art (yes - it is a "thing") and if you ask the receptionist or other guests at your hotel they can usually come up with a few good recommendations for you.
Of course, most people recommend free walking tours, museums etc. and these can be really good options if they are what you want to do, as they'll add to the experience of being in the new location.
To get more out of your free or paid for activities why not get better value for money and create some "micro challenges". Have a look at an activity you've already decided you want to do and add a small challenge to the experience - for example, if you're going to try somewhere new to eat, why not order something from the menu on the back of a recommendation, or better still, look for a busy eaterie and just give it a go.
A great, low cost way of getting a good feel for your new location is using the bicycle or scooter hire options you can find in most large cities. For very little money you can see more of the area than you would be able to on foot, and in most cases you can pick up and drop off in different places. All you'll need is a credit card, which you'll be able to use in one of the mulit-lingual machines (most are pretty easy to use). We've found this option a brilliant way of seeing cities from Cape Town to Vienna, although watch out for the backpedal brakes on the Austrian bikes!
Go for it - There's a world out there to explore!