You can't beat "C".

Travel to other stars means taking hundreds of years for each leg of the trip. There are many classic ways to make the trip. There are colonies in space where the grandchildren of the initial voyages are the ones to explore the next location. There are space traveling tombs where the occupants are in a near death hibernation. There are combinations of these two. There are voyagers who live for thousands of years so a few hundred years of playing playing checkers shuffle board and Karaoke at night is not a real hardship.

What happens to folks at home when a ship of exploration goes out and comes back a hundred years later. Who left alive cares? Maybe their hopes are too high and the ship finds nothing. Maybe the return day comes and nobody from either side shows.

A good recurring theme is the relativistic time dilation. A space traveler traveling at significant fraction of "C" ages slowly and will return to find society changed and all his friends dead and gone. This could be like a sleeper story or a time travel story. See Heinleins "Between Planets".

What if we sent robots out into space? Would this satisfy our desire to explore? What if the robots made more robots at each stop and made powerful relay stations to send back information from all of the stars visited? In 1000 years we'd be receiving feeds from hundreds, if not thousands of planets as robots spread through the universe. What if aliens took over the network and started changing the purpose of the robots.

What if we found a network started by aliens thousands of years ago and started using it for our own purposes?

Who would want to go into space? Would space travel be like a Botany Bay where criminals were given sentences of life aboard a slow boat to Vega?

What would happen to the space colonies after they've been traveling for a couple of generations and the lights go out and there are no light bulbs left? What if they change their minds about half way through? What if they are get to a planet and find that other earth travelers have been there and it takes only 3 hours to travel 100 light years instead of 1000 years?

Would robots get bored after 1000 years of space travel?

Weird Science

Worm holes and Bell's Theorem and Black holes and their like are liable to be replaced by strange new variations of string theory and alternative approaches to science.

There's a nut on the internet who claims that he's found a mistake in general relativity. What if he's right?

What if string theory comes up with a cheap easy way to get from here to there? What if Bell's Theorem allows information to travel faster than the speed of light? You don't get something for nothing. If a way to beat C is the "pro" what is the "con"?

One of my favorite ideas is: what if there is new prediction of some advanced physics that will allow free power or faster than light travel of time travel, but it could also cause an explosion as powerful as a super nova? Would you try it? Could it be that the occasional super nova we observe is actually an intelligent race running across the same formula and deciding to give it a try?

What about something really silly like Invisibility paint or ant-gravity paint or anti-gravity socks or a matter destroying ray or a ray that acts like x-rays but allows you see back in time? This is the grist of old time gadget oriented SF from the 40's and 50's. Gadget stories are always entertaining and need only have a tenuous connection to real science. The weirdnesses of quantum and string theory make a whole host of things sound plausible.

Idea 3.

Super Communication

We can send and receive more and more information. As we learn more about physics and electronics we can process more and more.

The question becomes what will we want to say and who will we want to say it to?

Cell phones are everywhere. Soon we will have cell video phones and soon we will all have chips injected near our ears directly into the mandible. I don't want to own a cell phone. I sometimes take my phone off the hook for days at a time. Will our children want or even be given a choice like that. Will some families have a phone injected in their child the way some families get their baby girls ears pierced before their first birthday?

In an an age when we can talk to anyone at any time, what do we have to talk about? I see people walking down the street having casual and even meaningless conversations on a cell phone. We can increase the quantity of talk, but will there be any move to increase the quality of talk.

What if there was a filter that could filter out the blah-blah-blah from conversations and would automatically answer "uhuh" to any meaningless conversation but still alert the user when something new was said. How about a compression routine similar to MP3 compression that could squeeze out the "no meaningful content" part of a conversation before transmission and then at the other side reinsert something similar without the users even knowing it was happening?

If we scan the skies with SETI and similar programs will we become sophisticated enough to hear another race speaking to us. What will they say? What will they say to us that means anything to us? If we record alien messages, who will decode them? Who is capable of understanding what an alien context is? What could we reply?

If we could put a voice box in a dog or cat that could receive it's thoughts and translate them into English, what would they say? Would they be able to communicate more information than a cat can with a wink and nod? (See Saki's great short story "Tobermory") Would the cat only say "I'm Hungry" over and over again? Would the Dog say "You smell like piss" all the time?