The areas of Senegal very close to the Gambia north and south really aren't much different from the Gambia - the Casamance to the south is a very popular destination for the French but you wouldn't get there and back in a day from Gambia. And what is there? Mangrove swamps, creeks,birds and beaches - well, apart from some French atmosphere and cuisine you will get all that in the Gambia!
If you just want to have been into Senegal there are day trips to Fathala Wildlife reserve run by Gambian tour agencies. You might possibly get a taxi to take you there from Barra if you didn't want an organised trip but that leaves the problem of getting around in the park. I have also been told that Gambian drivers don't particularly like driving into Senegal because of the "hassling" they receive - hence why many taxis just go to the border where people change taxis - but this is only a few miles in so it may be ok. The "park" sounds a bit "contrived" with a lot of introduced species, but could be pleasant enough - you are not in East Africa or Zambia so you can only see what there is to see! A trip advert (and other examples of organised trips in Gambia but many of those you could certainly do yourself if you wanted) -
http://www.gambia.co.uk/Docs/Gambia-Holidays/Excursions/Circle-Of-Life.aspxAnd from this description make up your own mind if it something you want to go on!
http://www.travelblog.org/Africa/Senegal/Tambacounda-Region/Tambacounda/blog-391084.h tmlRe the trip along the northern route to the circles - It doesn't seem to be "on offer" by the Gambia holiday site above but that doesn't mean it isn't possible. I found these detailed road maps of The Gambia which show the Stone Circle sites very well if you relate them back to the UNESCO files.
http://www.accessgambia.com/map.htmlThe map titled "Saloum" etc shows the location of Kerr Batch and Wassu -the 2 Gambian sites.
Of course you could try to kill 2 birds with 1 stone by visiting the Senegalese Stone circles!! It sounds as if Sine Ngayele is the best bet and that is near to Kaolack -about 50kms north of the Fathala Reserve. See photo/map etc
http://www.geckogo.com/Guide/Senegal/Western-Senegal/Kaolack/Whether it is practical you could only establish "on location"!