1. Modern people tend to travel more because we are more interested in the world outside of our own country because we have more access to all kinds of information. Also, all means of transportation became more accessible to all kinds of people - technology development made transport cheaper, faster and overall more effective. Thanks to this traveling became easier.
2. Mostly this depends on how big of a budget tourist has for their traveling. But big sums of money are not a requirement - you can have lots of fun traveling even without them! You always can visit some museums, parks, beaches, flea markets and family restaurants. It's often recommended to check out places which are popular with locals - those tend to be interesting.
3. Ukraine has lots of interesting places of historical value. Kyiv's churches - like Saint Sophia Cathedral or Trinity Gate Church are one of the most famous in the world.