What kind of hills will you be doing. You'll want a minimum of 9 speeds & for hilly areas you'll likely want more. For some reason most brands these days offer models that jump from 7-spd to 27-spd with precious little in between. Your price of $400/bike won't get you much these days if buying new. You might want to keep an eye out for some good used bikes while you're shopping. Avoid Schwinn! Sadly, those are bottom of the barrel these days. The same can be said for most of the Walmart-ish bike brands. Diamondback, Fuji & Nishiki are on my don't buy list also. Jamis, as someone has already mentioned, as well as Raleigh, Giant & Specialized may all be better choices, especially if you have a good local bike shop who sells these. You could also look KHS. A local dealer sells these but I don't know much about them.
A flat bar road bike would work well for your purposes. The handlebars are flat so you're not hunched over when riding. These are usually designed to handle city streets, both smooth & rough, plus gravel & some dirt. While not meant for hardcore mountain biking, with a tire change you could have fun on the less strenuous trails. The real limitation for rougher trails is the width of the tires these can accept. Different manufacturers call these different things, including hybrid. (Avoid hybrids with knobby tires & shocks. You don't need a fake off-road bike.) You might find these listed as Street, Urban, Alternative Road or whatever else their marketing departments can dream up. These bikes usually have wider tires than traditional road bikes but not as wide as mountain bikes. Some have seats more like road bikes, but most dealers will work with you to swap out some components like seats. Usually you have to buy the new seat but at a discount & the dealer installs it.
Just going through things online & thinking back to our recent shopping for BF, here are some options:
- Jamis Allegro Femme
(Femme meaning womens' bike.) http://jamisbikes.com/usa/allegrofemme.html
It's another 27-speed, but is an aluminum frame. It's componentry may be down a notch from the Coda but that may not matter to your wife.
- Specialized Crossroads http://www.specialized.com/us/en/bikes/multi-use/crossroads/crossroads
Has 21 speeds.
- Giant Escape 3 http://www.giant-bicycles.com/en-us/bikes/model/escape.3/22180/83981/
Has 21 speeds.
- Jamis Coda Sport http://jamisbikes.com/usa/codaseries.html
This one would be my top pick. Though these start at about $500. It's a 27-speed with a CroMoly frame. CroMoly frames just feel more comfortable to me than super stiff aluminum frames, especially on rougher roads & gravel paths.
- Giant Escape 2
is $450. http://www.giant-bicycles.com/en-us/bikes/model/escape.2/22180/83980/
Has 24 speeds & upgraded components from Escape 3.
- Raleigh Cadent 1 http://www.raleighusa.com/bikes-open-road-endurance-and-fitness-cadent-1
It's just a 7 speed so no fun in hilly areas.
- Raleigh Cadent 2
is about $500. http://www.raleighusa.com/bikes-open-road-endurance-and-fitness-cadent-2
It's a 27-speed. It also has disc brakes.
- KHS Urban Xcape
is $500. http://khsbicycles.com/bikes/urban-xcape-15/
It's a 24-speed.