They do seem to become less active at night or if deprived of sunlight, and so it may be possible they draw their primary source of energy from the sun. Annie refused to go underground. There also seems to be types of wall titans.
It seems to me that titans are scared of underground and need of sunlight make them weak to underground. Is this true and if so why doesn't the humans try to colonize underground?
There is no evidence to suggest that being underground/confined spaces can actually be a weakness for Titans. However there isn't any evidence supporting the contrary as well.
A definite strategic disadvantage of underground transformation is obvious (due to the restricted space for movement and the lack of visibility).
However in the corresponding chapter, you would do well to notice that the Titan smashes the tunnel from outside, all too easily. So underground colonization is a definite NO.
There is also no hard evidence on whether sunlight is a primary source of power for Titans. If that were the case, then Annie's transformation in the forest would have degenerated (no/minimal sunlight there).
Also (as suggested by @mirroroftruth), the use of forests is mainly because of the better 3D maneuver environment. However from my perception, undergrounds are just as bad an environment for 3D maneuvers, as they may be for Titans.
The main weakness is the back part on the neck that what I want to say. Underground is not exactly weakness. How I want to compare is Levi fighting with Titan on plain ground without tree and building.
Why lead Titan to forest or underground ? Because they loose their power. No The main reason is full utilization of 3D maneuver gear. They are confined and they can't use their full potential and give benefit to Scouting Legion to use their 3D maneuver gear.
If you read answer and all the comment you would get the knowledge why Annie refused to go underground.
For the case of sunlight I can't confirm that sunlight give extra power or not but night means less visibility which apply for both human and titan. In Chapter 38 Castle Utgard there is night scene and Titan attack castle at night. But in Chapter 34 Warriors Dance face of Titan inside wall is covered so that daylight won't reach the titan.
Ymir turn into Titan at night to protect her friend from other Titan and to fulfill the promised made with Krista
And for underground colonization, it is bad idea the reason is as キルア says in the comment.
Would you want to live underground when a group of Titans could walk overhead and demolish your entire city with one jump?
I think the titans choose not to move around at night because if you read attack on titan before the fall recent chapters you'll see how when kuklo went to test the prototype for the 3-D maneuver gear he was still attacked by 3 titans they probably can only see when they're right on you but I think in the dark they can actually rely on smell and hearing which is how they attacked kuklo
