Off season = more savings
Skip popular summer vacation destinations in favor of somewhere off the beaten path - you'll avoid skyrocket prices, scams and long lines at tourist attractions while profiting from a more enriched experience. Bonus: traveling off season means less coworker competition for time off, making it more likely you'll get approved.
If you prefer cold weather over hot, visit Barcelona or Paris in winter - what could be more romantic than sneaking into a warm cafe to watch rain or snow fall on rustic streets?
Consider alternative lodging

Depending on your budget, you can also rent a private or shared room in a house or apartment. Travel with a friend and split the cost to further drive down prices. Increase your odds of a good time by seeking out hosts with 50+ positive reviews and connecting with them in advance.
Note: plan out which attractions you'd like to visit then choose a place based on its proximity to those attractions - there's no point saving money on location if you'll be spending more on transportation instead. A hotel might be more expensive up-front but can save you on taxi costs whereas a remote AirBnB stay might drive up transportation costs, so do your research.
Go local
Los Angelenos! You have a wealth of travel options available at your toes! Make a day trip out of visiting MOMA (Museum of Modern Art), Huntington Library or the Griffith Laboratory. Got a weekend? Spend it in San Diego, Newport Beach or Claremont.
There is so much to do in LA, it's a waste to spend all your time on Beverly Drive, Westwood or Century City. There is a huge world around you - open your eyes to expand your possibilities.