We'd also probably try to send probes. Hopefully intelligent, self replicating probes that will avoid contaminating any alien biological systems while gathering information and transmitting it back.

Of course, that would be an extremely long lasting project so we'd have to set up some way to collect the signal here at home for the next few dozen thousand years.

In other words, we will have some interesting questions to ask ourselves and interesting challenges to overcome.

Perhaps, for example, we could find a dead moon, planet or stable orbit nearby (to avoid contamination) and set up a station or artifact that any intelligent life that gets to the advanced stage of getting to that body would find. We could have information about ourselves and instructions on how to communicate with us.

We could even do this for all candidate planets -- whether we know that they have developed intelligent life or not, yet. Basically lay out a galactic internet protocol so that even if these things are discovered long after we are gone, they could attempt to communicate with others that have found any of the other protocol monuments.