Can you put Hardwood and Tile next to each other?
Definitely. Except, you'll need to plan for a transition in between or there could be consequences.  For example, if Hardwood is butted up to Tile and installed very tightly, moisture or heat could cause the Hardwood to buckle if it doesn't have room to expand and contract. Don't worry, there are plenty of beautiful options available so you won't have to sacrifice style for function.

Install Hardwood Before Tile
If you are installing both materials, plan to put the Hardwood in first. Wood has a very definite thickness, whereas Tile's height can more easily be adjusted using setting materials to make the height difference more subtle. This allows you more options for transition materials.

Alternatives to standard floor transition strips

Schluter has come out with a number of thin, metal transition pieces that can be used as a break between flooring materials that will accentuate the desired aesthetic.

There are a number of mosaic tile sheets that can be made into strips to add some fun to your floors.

When you use planks from your hardwood floors as a transition piece, it creates a seamless look.