I found out it was a matter of being proactive. It wasn't that my friends didn't want to do anything with me. It was more that they, too, were waiting for a message or phone call or that they didn't know what to do with their time, either. Or they were having a busy week or something. So, everyone gets to take a turn at making the plans sometimes. At times, it may be frustrating if a lot of people happen to be busy on the date you're planning for or something like that. But, often, others will jump at an offer to do something with a friend if given the opportunity and time to plan for it. Other times, going out may not be an option for someone but an in-home visit might be. So that's something else to consider.
It may take some practice to find things that people like to do and to get good at the timing. I'm still working on it, myself. So be flexible with your plans. Be willing to go roller skating or to the movies on a different night. Or be willing to drop by for a chat instead of going out to dinner. And money is often a consideration, as well (both for yourself and for your friends). Be willing and creative enough to make plans that do not involve money. There are lots of possibilities.
Don't be afraid to make the calls and send the messages! People will often be glad you called even if they're not available to socialize. And this will build your relationships as well, as you get to know your friends by chatting over the phone or through other correspondence.
And if going out when you're ready just doesn't work for anyone else's schedule, don't be afraid to go out on your own once in a while. A lot of activities you enjoy with your friends can also be enjoyed with just yourself (see the "Having Fun" and "Home Hobbies" pages above). This can also be an opportunity to explore things that would be fun to do with friends as well as to get ideas for those "economical" activities.