While I’m a big advocate for bear spray and carry it when I go to Yellowstone, I don’t carry it around CdA. There are local places to buy it if you are headed over the mountains to Glacier NP, Yellowstone or Grand Tetons. The place I last bought mine is North 40 which is north on Government Way to Margaret Av ( just turn like you are going to enter the 76 gas station).
One of the prettiest and easiest hikes is Tubbs Hill, right in town. You start at McEwan Park. You can also do easy walks along the lakeshore. If you want to add some hill, go to the end of East Coeur d’Alene Lake Dr to Higgins Point and walk up there. The I90 road noise is annoying, though!
Another easy trail just north of town is English Point National Recreation Trail. There are a number of loops on either side of the road ranging from just under a mile to 3 miles or so.
Just out of town and more uphill is Mineral Ridge trail east of town off I90 at the Wolf Lodge Bay exit and south on ID 97.
https://www.blm.gov/visit/mineral-ridge-scenic-area-and-national-recreation-trail
Hope you enjoy the area!