You have two different options. One is to keep the bike as is and simply rebuild both wheels around the old hubs. If you think the hubs are near the end of their service life, then find some good quality used shimano hubs. Alternatively you could go with a freewheel based set up and find a seven speed freewheel.
The other option is to go with a modern wheelset which will be spaced at 130 mm (your old bike is probably spaced at 126 mm). It's no big deal to do this but you may want to talk to a shop. Then you can go 8-9-10-11 on the back. Your downtube shifters won't index. Also you will probably find that friction shifting with 10-11 on the back is a less than happy experience. Personally I'd go for a new 130 mm wheelset and go for 8, 9, or 10 on the back with new downtube shifters matched to your set up.
A bike shop can take you through this without too much hassle.