Yes, there will be an abundance of taxis waiting for the final Surfliner at downtown San Diego. After detraining, you go through the station to Kettner Street, and the taxis will be lined up across the street, to your left (northeast side).
The ride to Hotel Circle will take about 10-15 minutes at that hour, and cost between $20-$25.
Old Town is much, much closer and the stop there is at the Old Town Multimodal Transit Center but because of the late hour (and the fact that all transit buses from that center will have stopped running for the night by that time) there probably will not be taxis waiting. (Not that many people get off the Surfliner there at that hour.) There is a phone to call a taxi dispatcher along Old Town Avenue, but as you are a female traveling alone, I recommend the downtown San Diego station even if the taxi fare will be substantially higher.
Have no worries about the location of the Howard Johnson being unsafe. It's on the Hotel Circle south frontage road, alongside the Interstate 8 freeway, and is one of numerous hotels on both sides of I-8. As long as you have friends driving you, you have no concerns. Without a car, though, you would be facing a long walk just to get to a bus stop to begin a journey. Hotel Circle is not generally a place where people stay who don't have access to a car.
Happy traveling!