St. Petersburg is such a wonderful city; it is definitely worth the effort , if you can make the arrangements you need . I think it rivals Paris in beauty. If you are going to do it, you will have to plan ahead, since getting a Russian visa is not particularly cheap and is fairly complicated. Go ahead and send for the visa right now, as soon as you have partial arrangements made, and on the forms give the broadest possible range of dates that you might travel, in case your plans have to be changed. Plan as many days for the city as you can possibly arrange; five or six would not be too many, two or three would certainly be too few.
You should check the itinerary for GCT's Russia Revealed trip to give you an idea of some of the things you might want to see in St. Petersburg. Plan a day for an out of town one day excursion to Peterhof, a day (not consecutive) for another out of town excursion to Catherine's palace, and a full day (or, even better, two half days) at the Hermitage, if you can. Plan on a short trip on the canals, a visit to Yusupov Palace, a visit to the old fort , visit the top cathedrals, and perhaps a basic city tour. Remember that, as far north as it is, St. Petersburg will still be fairly cool in April, and you will probably have some rain. Early bulbs will be blooming in the palace gardens if you are lucky. It will be a wonderful visit for you, in a very special city.