What Cogman and Foxery said were very spot-on.
For now, we have one baseline for what life is, and where it comes from: Earth life.
Finding evidence of it elsewhere in the solar system would be an incredible discovery. It could help us learn about how life came about in the first place, how long it might take for it to arise naturally, and what other forms it may take.
Mars is just a first step, and is selected because it's a hospitable place for our probes, it's relatively nearby and easy to get to, and it has water, either in the form of ice at the poles or below the surface, or in the form of various hydrates in the soil.
There are other locations that would be of interest:
- Jupiter's moon, Europa. It's thought to have a large sub-surface ocean of water. Exploration problems: No atmosphere, so no parachutes to slow down a lander, meaning it would require the use of rockets. Rockets means more fuel, and a more complex spacecraft. The radiation environment at Jupiter is also quite intense, requiring specially hardened electronics. Finally, there's the matter of the icy crust, which could be miles thick, and is hard as solid rock. Drilling or melting through it would require a lot of hardware, and either way, a lot of energy.
Such a place has some very interesting elements for life:
- A large ocean to allow all kinds of mixing and particle interaction.
- Chemical energy from compounds dissolved in the water, or erupting from vents on the floor, similar to those on Earth's deep oceanbeds.
- Thermal energy, generated by tidal forces that constantly contort all of Europa - these are the same forces that create enough heat to liquefy sulfur and other substances on the moon Io, creating the largest volcanic eruptions in the solar system.
- Saturn's moon, Enceladus. Jets of frozen water mist were found spewing out from large cracks in the moon's southern hemisphere, hinting at the presence of reservoirs of sub-surface water.
- Titan, also at Saturn. Not so much a place to look for life, but a place to look at a location that could hold (frozen) precursors to it. The surface is covered with liquid hydrocarbons.
- Triton, at Neptune. Geysers, or perhaps "cryovolcanoes" were glimpsed by Voyager 2. A dedicated mission there, at least in the near-term, is unlikely simply because of the great distance. Cassini, sent to Saturn, was already a Flagship-class probe, the largest and most complex device we've ever sent to another planet. About half of its launch mass was fuel, a majority of which was needed to slow it down enough to enter orbit at Saturn. I don't know much about orbital mechanics, but since Neptune is much less massive than Saturn, slowing down to enter orbit would require even more fuel.
Out of all of them, I would most like to see more missions to Europa, orbiters at the very least. I think it has the best chance of anywhere else in the solar system of having something alive today, as opposed to somewhere like Mars, where we'd be more likely to only find fossilized remains. (Though fossilized remains would still be an incredible discovery.)