Interesting, the OPs question threw me a bit, first it was about WiFi, then MiFi, one dependent on the site's WiFi Signal Strength from an omnidirectional antenna, the other dependent on the Mobile Phone Signal.
It really depends on what devices the OP is attempting to use, and how mobile the devices might be.
At the simplest level, your mobile phone should be able to share either WiFi or GPRS/3G/4G connectivity, using Bluetooth. An iPhone usually requires some sort of pre-arranged and paid for means to share with up to three devices on Bluetooth, but an Android Phone will likely have this facility available for free.
Buying the MiFi seems to be the belt and braces method, of having a specific device for the purpose outlined above, which requires power.
Then there's the WiFi Signal Booster, another cheap solution, which requires power.
The complicated option is to either use a WiFi Access Point as a Bridge/Switch, with the onsite WiFi, or the purchase of e WiFi Bridge/Switch, or indeed both. One such device would provide WiFi Access to the onsite Network and allow all other devices to connect using Cat5e Cables, but using two devices would allow you to share WiFi on your own Private Network, and forward this to the onsite. This all sounds more complicated than it need be, but would be more appropriate if you were a heavy data user., and had Mains.
You might also only have one device you wish to connect onsite via WiFi, which would have a simple solution if it normally used a BNC connector for gaining a WiFi Signal from a rubberised whip omnidirectional antenna.
This latter scenario could effectively be solved without using any additional power by merely connecting a length of antenna cable to where the BNC rubberised antenna normally fits, and leading that cable outside to a directional yagi 2.4GHz antenna, normally about 12 inches long and giving 13dB of gain (compared to a whip of about 3dB), with all the signal directed at the WiFi Source onsite. This can effectively give line-of-sight WiFi of miles rather than yards, you might even get better connectivity pointing your yagi at a neighbouring caravan site...
So you can see, the question is not specific enough to be able to answer, but I've outlined the various options.
Facebook
Twitter