Laura, if you have access to a gym....

My two favorite core exercises are decline sit ups and back extensions. I try and make sure my stomach is tight the whole time I'm lifting and then I always do decline sit ups and back extensions at the end. I go to the gym 2-3x per week right now so core work is the same.

Decline sit ups are fantastic because they work your overall trunk similar to planks with the added ab work. But most specifically, I love them because of how much they also work your hip flexors!! Oh baby that's some good stuff, especially for cycling/cyclists. These are done on a bench where you lay on your back and it's angled down towards the ground. Your feet/knees are higher than your head. They generally have one or two big foam rollers to throw your feet behind. If you want to do these, make sure the angle is not steep. Your hip flexors will probably get pissed off at first but the more you do them, the stronger they (and your core) will get.

Back extensions, I find, are imperative. Without doing these, I would never be able to ride aero on the hoods or down in my drops at a really hard pace. These work your spinus erectus muscles that parallel your spine, especially down by your lumbars. These are done on a little platform that's at a 45 degree angle. There's two platforms for your feet and a large pad where your hips rest against. The height setting for the pad should be tall enough so that your body weight rests in a comfortable spot at your hips. Too low and your weight will be all on your quads (and it hurts). These are done slowly both bending up until your back is straight (so your whole body will be at a 45 degree angle in a straight line) and then bending at the hips back down. That's some good stuff too.

Good luck!