Berne is mostly farmland from what I saw and though very nice Lucerne would be better.you can visit several mountains in the Swiss " Alps" chain like Pilatus ,Rigi or Stanserhorn each with their own unique character and mode of transport .Besides Lucerne itself is very scenic .April would be a great month to visit
Canton Bern indeed has a lot of farm country, but includes a great variety of geographies. Much of the Emmental region is in Canton Bern, and hiking or walking there is very popular amongst the Swiss. The "Big Name" alps, in the Bernese Highlands ( Berner Oberland) are obviously in Canton Bern. For that matter, Canton Lucern has a lot of farm country, too.
The city of Bern itself is the capital of Switzerland. It is not a farm. ;-)
The arcaded old town is worth a detour. It does not have the overall beauty and character of the city of Lucern, which gains a lot from the lake and the surrounding mountains.But, it does have a lot to see, and is well worth a stop over on a train ride going through or a day trip from elsewhere. In April, the Rosegarden will not be the attraction it is in June or the Summer, but the walk to it from the Bahnhof is a nice stroll, and the views of the city from the Rosegarden are quite nice..
I support your comments about Lucern as a preferred destination for a first time visitor. If you go in the high season, a lot of other people from all over the world are demonstrating that they believe it, too.