Since giving up my car I am a lot more concerned about finding a secure place to park my bike, I have a New York Fahgettaboudit lock which by all accounts is practically indestructible but there's alway the chance some scumbag will nick the front wheel, saddle or just damage the bike out of malice.
Fortunately in the last couple of years cycle parking in the area has improved a lot.
Q-Park at Liverpool ONE
They have a secure cycle room located on the ground floor, easiest access is from Thomas Steers Way, at the bottom of Kenyon steps, opposite the Hilton.
To gain access you will need a swipe card which can be had from the office, go through the double doors in the picture above and the office on one the right, fill out a little form and they will give you your card to keep. It is free to use, which is very satisfying as it is a rather expensive car park (£7 for three hours). Barrier entrance, double tier racks and CCTV.
Liverpool Lime Street Station
These have just been installed in the last few weeks, outdoors but undercover, they are called streetpods. I've not seen them before but they look pretty good. You put the bike in forwards and lock the rear end and the large plastic shell prevents the front wheel being removed. It also helps to keep it upright, preventing damage.
Not available in town but these have been popping up at a few overgound Merseyrail stations as part of their Cycle Scheme this one is at Waterloo.
Send in an application and they send you a swipe card for the bike shed at a station of your choice, you are only allowed to use it at one station apparently, but it's free and the facility is good. Secure, undercover, well lit, CCTV inside and also little cages in racks for you to put helmet/gloves etc.
If you know of any other good ones give me a shout.